
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
Points \( A_{1}, B_{1}, C_{1} \) are the midpoints of the sides \( BC, AC, \) and \( AB \) of triangle \( ABC \), respectively. It is known that \( A_{1}A \) and \( B_{1}B \) are the angle bisectors of angles of triangle \( A_{1}B_{1}C_{1} \). Find the angles of triangle \( ABC \).

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