
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
Consider a triangle  $ABC$  with  $\angle ACB=120^\circ$ . Let  $A’, B’, C’$  be the points of intersection of the angular bisector through  $A$ ,  $B$  and  $C$  with the opposite side, respectively.
Determine  $\angle A’C’B’$ .

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