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This is how I think of the words 'form' and 'formulate', please correct me if I'm wrong:

Form is to create out of nothing and formulate is to create from that which is already formed (i.e. created)
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No. Formulate generally has more to do with chemistry and with creating ideas. Form generally has more to do with wood, clay and iron.
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So, do you "Formulate a committee of advisors" or "Form a committee of advisors" ?
Form a committee of advisors

Do I form an agreement with another party or do I formulate the agreement?

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anonymousDo I form an agreement with another party or do I formulate the agreement?

Neither; you 'make an agreement' or 'come to an agreement'.