16 types
INTJ and ENTJ
INTJ and ENTJ both want a result that would survive being looked at later. ENTJ will organise the room, including the bits nobody claimed, and likes a goal with a date on it. INTJ would rather hold the plan in private and skip the part where the room watches it being organised.
ENTJ moves fast and needs to leave a note so the careful people can follow. INTJ is one of those careful people, and will not accept a goal whose constraints were improvised in the corridor. Warmth from ENTJ lands better when it is specific. Reliability from INTJ lands better when the plan is said out loud, not implied by a silence that ENTJ reads as agreement.
Split the work by what each of you is actually for. ENTJ can own the date, the owner, and the conversation that gets other people moving. INTJ can own the standard and the long problem. If both of you try to run the room, you will spend the week correcting each other's method instead of finishing the thing.