
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
Let point $P$ be a point on the hyperbola $\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1$ ($a > 0$, $b > 0$), and let $F_{1}$ and $F_{2}$ respectively be the left and right foci of the hyperbola. It is known that $PF_{1} \perp PF_{2}$ and $|PF_{1}|=2|PF_{2}|$. Calculate the eccentricity of the hyperbola.

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