
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 $F_{1}$ and $F_{2}$ are the foci of a pair of related curves, and $P$ is the intersection point of the ellipse and the hyperbola in the first quadrant, when $\angle F_{1}PF_{2}=60^{\circ}$, determine the eccentricity of the ellipse in this pair of related curves.

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