The "and" in "try and..." may be a shorthand for the material implication of two temporal modal paths:

"try and X" = can X -> must X = not can X or must X

That said, the word "both" doesn't collocate before "try and X" because it instead pushes us toward an interpretation as logical conjunction:

"both try and X" = can X and must X

Likewise, despite the usage of "try not to", the phrase "try not and" doesn't show up, because under material implication the phrase becomes nonsense:

"try not and X" = not can X -> must X = can X or must X

OTOH "you mustn't try and X" sounds plausible, which tracks.