
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 that $F_1$ and $F_2$ are the two foci of a hyperbola, a line perpendicular to the real axis and passing through $F_2$ intersects the hyperbola at points $P$ and $Q$. If $\angle PF_1Q= \frac {\pi}{2}$, calculate the eccentricity $e$ of the hyperbola.

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