
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 triangle  $ABC$  is isosceles with  $AB=BC$ . The point F on the side  $[BC]$  and the point  $D$  on the side  $AC$  are the feets of the the internals bisectors drawn from  $A$  and altitude drawn from  $B$  respectively so that  $AF=2BD$ . Fine the measure of the angle  $ABC$ .

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