
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 foci of an ellipse are $F_{1}(0, -\sqrt{3})$ and $F_{2}(0, \sqrt{3})$, with eccentricity $e= \frac{\sqrt{3}}{2}$. If point $P$ is on the ellipse, and $\overrightarrow{PF_{1}} \cdot \overrightarrow{PF_{2}}= \frac{2}{3}$, find the size of $\angle F_{1}PF_{2}$.

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