
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
For the ellipse $\frac{x^2}{4} + \frac{y^2}{3} = 1$, let the two foci be $F_1$ and $F_2$. A line passing through $F_1$ and perpendicular to the x-axis intersects with the ellipse at point $P$. Then, the length of $|PF_2|$ is _______.

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