
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
The rhombus  $ABCD$  is given. Let  $E$  be one of the points of intersection of the circles  $\Gamma_B$  and  $\Gamma_C$ , where  $\Gamma_B$  is the circle centered at  $B$  and passing through  $C$ , and  $\Gamma_C$  is the circle centered at  $C$  and passing through  $B$ . The line  $ED$  intersects  $\Gamma_B$  at point  $F$ .
Find the value of angle  $\angle AFB$ .

*(S. Mazanik)*

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