
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 an ellipse $\frac{x^2}{9}+\frac{y^2}{6}=1$, $F_{1}$ and $F_{2}$ are two foci, $O$ is the origin, $P$ is a point on the ellipse, $\cos \angle F_{1}PF_{2}=\frac{3}{5}$, calculate the value of $|PO|$.

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