
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 left and right foci of the hyperbola $C: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 (a > 0, b > 0)$, and point $P$ is on hyperbola $C$. If $PF\_1 \perp F\_1 F\_2$ and $PF\_1 = F\_1 F\_2$, find the eccentricity of hyperbola $C$.

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