This question tests the correct formation of the present continuous tense, which is often used to talk about future plans.
The structure for the present continuous tense is: Subject + am/is/are + verb(-ing).
Let's analyze the options:
(A) I am plan: plan is the base form of the verb, not the -ing form. This is incorrect.
(B) I planning: The auxiliary verb am is missing. This is incorrect.
(C) I am planning: This correctly follows the structure Subject (I) + am + planning (-ing form). This is the correct sentence.
(D) I am been planning: This is a grammatically incorrect combination of verbs. The correct present perfect continuous would be I have been planning.
Therefore, the only grammatically correct sentence is (C).