The form should __________ carefully.

This sentence requires a modal verb ("should") followed by a passive infinitive. When a modal verb is used in the passive voice, the structure is "modal verb + be + past participle". The form is not performing the action of filling; it is being filled. Therefore, "be filled" is the correct passive infinitive form. "Fill" (active infinitive) would imply the form itself is doing the filling. "Filled" (past participle without "be") and "filling" (present participle) are grammatically incorrect in this context following "should".