
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 $\frac {x^{2}}{4} + y^{2} = 1$, its two foci are F<sub>1</sub> and F<sub>2</sub>. If a line perpendicular to the x-axis passes through F<sub>1</sub> and intersects the ellipse, with one intersection point being P, then the length of |PF<sub>2</sub>| equals \_\_\_\_\_\_ .

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