
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 cyclic quadrilateral  $ABCD$  is given. The lines  $AB$  and  $DC$  meet at point  $E$ , and the lines  $BC$  and  $AD$  meet at point  $F$ . Let  $I$  be the incenter of triangle  $AED$ , and a ray with origin  $F$  be perpendicular to the bisector of angle AID. In which ratio this ray dissects the angle  $AFB$ ?

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