plan vs think out

plan is a noun but think out is not a noun.

Word	Noun	Adjective	Verb	Adverb
plan	Yes	No	Yes	No
think out	No	No	Yes	No

As verbs, think out is a hyponym of plan; that is, think out is a word with a more specific, narrower meaning than plan:

Other hyponyms of plan include aim, aspire, draw a bead on, shoot for, go for, hope.

plan (noun)	think out (noun)
scale drawing of a structure
a series of steps to be carried out or goals to be accomplished
an arrangement scheme

plan (verb)	think out (verb)
make plans for something	consider carefully and rationally
have the will and intention to carry out some action
make or work out a plan for; devise