
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 foci of the ellipse $\dfrac {x^{2}}{9}+ \dfrac {y^{2}}{2}=1$ are $F_{1}$ and $F_{2}$. Point $P$ is on the ellipse, and if $|PF_{1}|=4$, the size of $\angle F_{1}PF_{2}$ is \_\_\_\_\_\_.

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