
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given that point $A$ has coordinates $(-1,0)$, and point $B$ has coordinates $(1,0)$, and a moving point $M$ is at a distance of $4$ from point $A$. The perpendicular bisector of segment $MB$, denoted as line $l$, intersects segment $MA$ at point $P$. Find the equation of the trajectory $C$ of point $P$.

Present the answer in LaTex format: \boxed{Your answer}
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