
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
Let the vertices A and C of a right triangle ABC be on the arc with center B and radius 20. A semicircle with diameter [AB] is drawn to the inner region of the arc. The tangent from C to the semicircle touches the semicircle at D other than B. Let CD intersect the arc at F. What is |FD|?

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