Well, the participle form would be incorrect as it shows a continuous action, which, for reasons I cannot explain, is incorrect for this sentence.
And if you wonder why it is not the full infinitive, then go onto wikipedia, where it explains when the bare infinitive is used, instead of the full.
Also, the infinitive functions as a noun, adjective or adverb. In this case, think is a subject complement, and therefore it is a noun infinitive.
Does this make any sense to you?
