
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
There are rhombus  $ABCD$  and circle  $\Gamma_B$ , which is centred at  $B$  and has radius  $BC$ , and circle  $\Gamma_C$ , which is centred at  $C$  and has radius  $BC$ . Circles  $\Gamma_B$  and  $\Gamma_C$  intersect at point  $E$ . The line  $ED$  intersects  $\Gamma_B$  at point  $F$ . Find all possible values of  $\angle AFB$ .

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