Another June is in the books -- and, once again, the Mets aren’t sorry to see it go. Finishing the month with just 10 wins in 28 tries, the Mets fell seven games further behind the Braves in the National League East. They now trail nine teams in the NL Wild Card standings. Barring a spectacular early July run, those results all but ensure the Mets will be sellers prior to the July 31 Trade Deadline. As it just so happens, many of this week’s Inbox questions revolve around that fact. Let’s dig in:

Do you envision the Mets doing anything surprising this Trade Deadline?
-- @marissabaseball via Twitter

Of the more than 300 questions in this week’s Inbox, a good number dealt with the Mets’ Trade Deadline plans -- and rightfully so. Here’s a look at their most obvious trade candidates:

• Right-hander Zack Wheeler: The Mets almost have no choice but to trade Wheeler. While they could hang onto him and extend him a qualifying offer this winter, any resulting Draft pick compensation for him would not come until after Round 2. Odds are, they’ll be able to find a partner willing to offer more, making it imperative that they deal Wheeler this month.

• Third baseman Todd Frazier: Following an ice-cold April and a mediocre May, Frazier broke out with eight home runs in June. He could be a right-handed bench option for a contending team, giving the Mets a chance to receive some talent in exchange for him. If nothing else, they’d probably settle for shedding the final $3 million on Frazier’s contract.

• Left-hander Jason Vargas: Like Frazier, Vargas is an impending free agent who has recovered from a poor start to provide some midsummer value. Pitching is always in demand, meaning the Mets probably can find a trade partner if they look hard enough. The question is whether they’ll be willing to pay down the remainder of his $8 million salary. If so, will that be enough to reel in some value in return?

• Outfielder Juan Lagares: Once a promising part of the Mets’ young core, Lagares is enjoying a rare run of health this season, but he has provided little value in his final year before free agency. If there’s a contender out there willing to add Lagares as a late-game defensive replacement, the Mets -- who shopped the former Gold Glover unsuccessfully last winter -- would be all too happy for the salary relief.

• First baseman Dominic Smith: You’ll hear a lot about Smith this month because he’s blocked by All-Star Pete Alonso, but that doesn’t mean he’s likely to move. For most contenders, Smith would only be a left-handed bench bat, as opposed to a starting first baseman or outfielder. While the Mets almost have to consider trading him, it’s difficult to imagine them accepting a low-ball offer for a player with five more years of team control -- even if they don’t have an obvious place for Smith to play on the 2020 roster. This one could go either way.

• Righty Noah Syndergaard: The rumors that swirled around Syndergaard all offseason aren’t likely to cool now that he’s only a year and a half from free agency. Still, the Mets intend to compete in 2020, and they would be hard-pressed to do so without Syndergaard -- particularly if they trade away Wheeler and Vargas. Barring someone backing up the Brink’s truck for Syndergaard, the Mets have little choice but to hang onto him.

• Righty Seth Lugo: This is a long shot, but it wouldn’t be shocking to see the Mets field offers on Lugo, their most valuable reliever this season. Relief pitchers are notoriously fickle from year to year, and Lugo is about to get expensive; he’s due to hit arbitration for the first time this winter. And given that Lugo is pitching with a partially torn ligament in his right elbow, there’s an argument for selling high on him.

Everyone else on the roster either has too little value for a trade to be realistic or is too important to the Mets’ core. If the team decides to blow things up and attempt a full-scale rebuild, Michael Conforto, Jeff McNeil, Amed Rosario and others would be chips. But the Mets have given no indication they’re willing to go down that road.

If Wheeler and Vargas are traded, who fills those holes?
-- @BradyPSnyder via Twitter

This is where Justin Dunn -- gone to the Mariners in the Robinson Cano trade -- would have been useful. Fellow top prospect Anthony Kay isn’t quite ready for the Majors, and most of the Mets’ other most intriguing pitchers are in the lower levels of the Minors. If the Mets deal both Wheeler and Vargas, Walker Lockett would be a strong bet to fill one of those spots. The other could go to Chris Mazza, Drew Gagnon or even a veteran such as Ervin Santana or Hector Santiago.

The Mets could also try Lugo or Robert Gsellman in the rotation, giving them a couple of intriguing options heading into Spring Training. For now, file that under: “I’ll believe it when I see it.”

Is there any chance they extend a player in the offseason? And if yes, who (Alonso, Syndergaard, Conforto)?
-- @eddie_lennon via Twitter

All the players you mentioned are classic extension candidates, as are McNeil and Rosario. The Mets haven’t shown much willingness to talk extension with those types of players in the past, though, and Conforto is repped by Scott Boras, who generally encourages his players to hold out for free agency. While signing a long-term deal is always a possibility, I will -- again -- believe that sort of thing when I see it.

Like all Mets fans, I feel like the sky is falling. But when I take a step back. I realize that we'd be in the mix this year with an average bullpen. Since we have an inexpensive young core of position players, do you see a realistic path where we can be a playoff team in 2020?
-- @jonhurwitz via Twitter

The short answer is yes. The long answer is it will be difficult, and the reason why is starting pitching. Without Wheeler and Vargas, the Mets will have to fill two rotation holes this winter. Given how tight their payroll situation looks (many returning players are due salary increases), it’s tough to envision them shopping in the Gerrit Cole/Madison Bumgarner free-agent aisle. It’s also hard to see them competing for the playoffs without adding significantly to their rotation. They’re going to need to find a solution there if they want to be competitive in 2020.

Are they really going to keep Mickey Callaway the whole year?
-- @johnkil3041711 via Twitter

It certainly seems that way. There have been three or four inflection points when the Mets could have made a change at manager. Each time, general manager Brodie Van Wagenen has not only stuck with Callaway, but given him a public and emphatic vote of confidence. At this point, with the Mets out of realistic contention, there’s no longer much point in making a change; the Mets appear content to ride out the rest of the season with Callaway at the helm.

What do you think the long-term plan at shortstop is? Rosario clearly hasn’t developed the way Mets would have hoped.
-- @cbrody1121 via Twitter

As fun as it is to think about Rosario in center field, the Mets’ greater need is at shortstop. They’re a better long-term team if they figure out how to solve Rosario’s defensive woes. Offensively, Rosario hasn’t been elite, but he’s proven plenty good enough as a bottom-of-the-order hitter.

With Andres Gimenez struggling at Double-A Binghamton, the Mets don’t exactly have anyone knocking on the door to replace Rosario. Ronny Mauricio is the long-term answer fans can dream about, but until he’s ready -- probably around 2022 -- it’s either going to have to be Rosario or Gimenez at short.

Can the Mets benefit from an using an opener? It seems they’ve tried everything and they won’t be getting any new personnel to cure the bullpen woes.
-- @egomaintenance via Twitter

The Mets don’t really fit the profile of a team that would benefit from that strategy. With the exception of Vargas, their starters generally pitch deep into games. Given that almost all of their relievers have struggled, a game-opening assignment for one of them would also be potentially perilous. It’s not something you’re likely to see the Mets try.

If the Mets continue to flounder, do you think a Tim Tebow September callup is possible to try a produce a little late-season buzz?
-- @Elipshetz52 via Twitter

Tebow’s performance at Syracuse (.154/.233/.231, two home runs) doesn’t warrant it, but if the Mets are out of contention, that won’t much matter. Put it this way: It certainly wouldn’t shock me to see Tebow Time in Queens.