
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 $\dfrac{x^2}{36}+\dfrac{y^2}{b^2}=1$ ($6>b>0$) and any point $P$ on the ellipse other than the vertices, it satisfies $|\overrightarrow{OP}+\overrightarrow{OF}|=7$, where point $F$ is the left focus of the ellipse, and point $O$ is the origin of the coordinate system. Determine the value of $|PF|$.

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