#1 may be acceptable, and even grammatically justifiable, but only to a very few readers, none of whom are employed by the ETS®. This is germane because, as another answer points out, the question you cite is written under their aegis, and posed as: "Select the best answer to complete the sentence."
Your question is not so much about whether a given verb takes a particular form of complement, but about the appropriate use of a gerund, or participle, as an adjective. Not every verb's gerund is grammatical when used this way in every instance.
#4, the infinive to act, is the only proper answer, because, although the use of a verb as a gerund, participle, or adjective in English may seem "random" to a learning speaker, it is not, any more than is the assigning of gender in German.
Neal Whitman's Very Test provides an interesting method of assessing whether or not a given usage is grammatical.
Usage #1 seems to fail the Very Test.