So I got to thinking. In the core rulebook, it states that Spell-Like Abilities have no components, is unaffected by Arcane Spell Failure from armor even if it resembles an actual spell, and is completely a mental activation. In Occult Adventures states, that because all psychic spells(the type, not the class) use Emotion and Thought components and is completely mental, spells can be cast even while the caster is pinned or paralyzed. So this raises the question: Is it possible to use a Spell-Like Ability while paralyzed or otherwise incapable of movement?
This is a Pathfinder 1st Edition question, so I flagged it to be moved to the PF1E Rules forum instead of the 2E one.
To answer your question: Yes, SLAs are purely mental, so you can use them while paralyzed or otherwise only capable of mental actions. The relevant text is:
(...)A spell-like ability has no verbal, somatic, or material component, nor does it require a focus. The user activates it mentally. Armor never affects a spell-like ability’s use, even if the ability resembles an arcane spell with a somatic component.(...)