
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 $C$: $\frac{x^2}{9}+\frac{y^2}{5}=1$, with $F_1$ and $F_2$ as the left and right foci, and $P$ as a point on the ellipse, satisfying $\cos \angle F_{1}PF_{2}=\frac{1}{4}$, calculate the length of $|OP|$.

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