
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 tangent line passing through a point  $A$   outside the circle with center  $O$  touches the circle at  $B$  and  $C$ . Let  $[BD]$  be the diameter of the circle. Let the lines  $CD$  and  $AB$  meet at  $E$ . If the lines  $AD$  and  $OE$  meet at  $F$ , find  $|AF|/|FD|$ .

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