
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 hyperbola $\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1$ ($a>0$, $b>0$), a line passing through the origin with an inclination angle of $\frac {\pi}{3}$ intersects the left and right branches of the hyperbola at points P and Q respectively. A circle with the segment PQ as its diameter passes through the right focus F. Find the eccentricity of the hyperbola.

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