
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 a triangle, the side \( a \) and the two adjacent angles \( \beta \) and \( \gamma \) are known. Find the angle bisector drawn from the vertex of the third angle.

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