The English grammar concept where the second verb in a sentence uses the base form is primarily related to the use of:

Modal Verbs:

Modal verbs (can, could, may, might, must, shall, should, will, would) are always followed by the base form of the main verb.
Example: She can sing beautifully.
Verbs of Perception:

Verbs like see, hear, watch, feel, notice, observe are often followed by an object and then the base form of a verb to describe the action that was perceived.
Example: I saw him leave the house.
Causative Verbs:

The verbs let, make, and have (when used in a causative sense) are followed by an object and the base form of a verb.
*Example: He made her laugh.
Other Constructions:

There are also some other specific constructions where the base form is used, such as after the expressions had better and sometimes after the verb help.
Examples: You had better go now. / Can you help me move this box?
Additional Notes

The base form of a verb is its simplest, uninflected form, as it appears in the dictionary.
In these constructions, the first verb (modal, perception, causative, etc.) carries the grammatical information about tense, mood, etc., so the second verb remains in its base form.