In your maintenance phase, pay or destroy Mine Picket.
Your opponent must pay 1 at the beginning of their sortie phase; if they can't, they skip their sortie phase.
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Explained
In your maintenance phase, pay or destroy Mine Picket.504.3
Each of your maintenance phases, once your cards are ready: pay it with any steam, or the base goes to your scrapyard. If you can't pay, it is destroyed (504.3).
Your opponent must pay 1 at the beginning of their sortie phase; if they can't, they skip their sortie phase.701.5
As their sortie phase begins, their steam pays it at once; they don't choose. Without the steam, the whole phase is skipped: no windows, no dispatch, no battles, for either player (701.5).