
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
In triangle  $ABC$ , the angle at vertex  $B$  is  $120^o$ . Let  $A_1, B_1, C_1$  be points on the sides  $BC, CA, AB$  respectively  such that  $AA_1, BB_1, CC_1$  are bisectors of the angles of triangle  $ABC$ . Determine the angle  $\angle A_1B_1C_1$ .

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