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In Solo Mode, does a revealed Completed Plan card count as a finished plan if the AAA does not score it?
No. A plan is completed only when it is scored. A revealed card the AAA does not score changes nothing: it does not flip your plan card to its approved side, does not count toward ending the game and does not trigger the reshuffle. Check the tick marks in the top-right corner of the AAA architect card; a plan counts only if the matching Completed Plan card is drawn in a position that has a tick.