
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 the right focus $F$ of the ellipse $\frac{x^{2}}{25}+ \frac{y^{2}}{9}=1$, draw a line with an inclination angle not equal to $90^{\circ}$ intersecting the ellipse at points $M$ and $N$. The perpendicular bisector of chord $MN$ intersects the $x$-axis at point $P$. Find the ratio $\frac{|PF|}{|MN|}$.

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