
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 ellipse C: $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a > b > 0)$ have its left and right foci as $F_{1}$ and $F_{2}$, respectively. If point P on C satisfies $PF_{2} \perp F_{1}F_{2}$ and $\angle PF_{1}F_{2} = 30^{\circ}$, determine the eccentricity of C.

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