
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 $C:\frac{{x}^{2}}{{a}^{2}}-\frac{{y}^{2}}{{b}^{2}}=1 (a > b > 0)$ with left and right foci ${F}_{1},{F}_{2}$ respectively. A circle with center ${F}_{2}$ and radius ${F}_{1}{F}_{2}$ intersects the right branch of $C$ at points $P,Q$. If one of the internal angles of $\mathrm{\Delta }{F}_{1}PQ$ is ${60}^{0}$, determine the eccentricity of $C$.

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