
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 circle $F\_1$: $(x+2)^2 + y^2 = 36$, fixed point $F\_2(2, 0)$, $A$ is a moving point on circle $F\_1$. The perpendicular bisector of segment $F\_2A$ intersects the radius $F\_1A$ at point $P$. Determine the equation of the trajectory $C$ of point $P$.

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