
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 a moving circle $P$ that is tangent to the circle $E: (x+\sqrt{3})^2 + y^2 = 25$ and internally tangent to the circle $F: (x-\sqrt{3})^2 + y^2 = 1$. Let the locus of the center of the moving circle $P$ be the curve $C$.

1. Find the equation of the curve $C$.
2. A line $l$ intersects the curve $C$ at points $A$ and $B$. $M$ is the midpoint of segment $AB$. If $|OM| = 1$, find the maximum area of triangle $AOB$.

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