
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
\( AB \) is the diameter of a circle; \( C, D, E \) are points on one semicircle \( ACDEB \). Points \( F \) and \( G \) are taken on the diameter \( AB \) such that \(\angle CFA = \angle DFB\) and \(\angle DGA = \angle EGB \). Find \(\angle FDG\), if the arc \( AC \) equals \( 60^\circ \) and the arc \( BE \) equals \( 20^\circ \).

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