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So, if it refers to adjacency to the card and not the MHQ, how do you know which die to use when rolling to "seize control of an adjacent base?" I have read other threads here that say you still must be adjacent to you MHQ. I would love to get a definitive answer to this.
MHQ presence on or adjacent to a Facility is a different rule independent from each individual card text.
Here is an example. Let's say that a card says:
"You may Seize Control of an adjacent facility". Where you choose to place that Facility on the board will determine which facilities will count as adjacent. Then, after placing the card on the board, as a totally independent rule, in order for you to be able to perform the Seize Control action, you also need to have an MHQ present on or adjacent to the facility you are targeting.
I hope this helps.