
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 trapezoid  $ABCD$  inscribed in a circle  $O$ ,  $AB||CD$ . Tangent at  $D$  wrt  $O$  intersects line  $AC$  at  $F$ ,  $DF||BC$ . If  $CA=5, BC=4$ , then find  $AF$ .

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