
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 a point $P$ on the hyperbola $\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1 (a > 0, b > 0)$, let ${F\_1}, {F\_2}$ be the left and right foci of the hyperbola, respectively. If $\angle {F\_1}P{F\_2}={90}^{0}$ and $| P{F\_1} | = 2 | P{F\_2} |$, then the eccentricity of the hyperbola is $(\ \ \ )$.
A) $\sqrt{2}$
B) $\sqrt{3}$
C) $2$
D) $\sqrt{5}$

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