
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
One focus of the ellipse \(\frac{x^2}{4} + y^2 = 1\) is at \(F = (\sqrt{3}, 0)\). There exists a point \(P = (p, 0)\), where \(p > 0\), such that for any chord \(\overline{AB}\) passing through \(F\), the angles \(\angle APF\) and \(\angle BPF\) are equal. Find \(p\).

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