
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 that $P$ is a point on the ellipse $\frac{x^2}{25} + \frac{y^2}{b^2} = 1$ ($0 < b < 5$) other than the vertices, and $F_1$ is the left focus of the ellipse. If $|\overrightarrow{OP} + \overrightarrow{OF_1}| = 8$, calculate the distance from point $P$ to the left focus of the ellipse.

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