
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 the ellipse $C$: $\frac{x^2}{4} + \frac{y^2}{3} = 1$ with its right focus at $F$, and a line $l$ that is not perpendicular to the $x$-axis and does not pass through point $F$, intersects the ellipse $C$ at points $M$ and $N$. If the external angle bisector of $\angle MFN$ intersects line $MN$ at point $P$, find the $x$-coordinate of point $P$.

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