
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
A line passing through the right focus F of the hyperbola $\frac{x^2}{9} - \frac{y^2}{16} = 1$ at an angle of $\frac{\pi}{4}$ intersects the hyperbola at points A and B. Find the distance from the midpoint C of the line segment AB to the focus F.

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