
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
The angle between the sides of a triangle, whose lengths are \(a\) and \(b\), is \(\varphi\). Find the length of the segment of the bisector of this angle that lies inside the triangle.

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