
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 O be the coordinate origin, $F_{1}$ and $F_{2}$ be the left and right foci of the ellipse $\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1\left(a \gt b \gt 0\right)$. If there exists a point P on the ellipse such that $\angle F_{1}PF_{2}=\dfrac{\pi }{3}$, and $|OP|=\dfrac{\sqrt {3}}{2}a$, determine the eccentricity of the ellipse.

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