The verb form of the adjective facile is facilitate. It is slightly different in meaning from the adjective, though. Facile usually means "easily done" or "easily said" but often with a slightly negative meaning e.g. "a facile statement" is an oversimplified, superficial one which shows no real grasp of the facts (e.g. "We need to reduce crime" could be called a facile statement, since it offers no analysis or helpful ideas.)
On the other hand, the verb to facilitate is neutral in meaning; it just means "to make easy/ easier; to further or help." For example, you might send someone a pre-addressed envelope to facilitate their reply to your letter.
The noun form is facilitation, and has the same meaning as the verb. A slightly different noun form is facility, which has the meaning either of easiness (e.g., fluency in speaking a language) or a service/ piece of equipment provided to make life easier (e.g. baby changing facilities in public toilets.)
All these forms come from the French word facile, "easy."
On the other hand, the verb to facilitate is neutral in meaning; it just means "to make easy/ easier; to further or help." For example, you might send someone a pre-addressed envelope to facilitate their reply to your letter.
The noun form is facilitation, and has the same meaning as the verb. A slightly different noun form is facility, which has the meaning either of easiness (e.g., fluency in speaking a language) or a service/ piece of equipment provided to make life easier (e.g. baby changing facilities in public toilets.)
All these forms come from the French word facile, "easy."