
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
The ellipse $C$: $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ has its left and right foci as $F_1$ and $F_2$, respectively. Point $P$ is on $C$ and satisfies $PF_2 \perp F_1F_2$, $\angle PF_1F_2=30^\circ$. Calculate the eccentricity of $C$.

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