
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 an isosceles triangle \(ABC\) on the base \(AC\), a point \(M\) is taken such that \(AM = a\) and \(MC = b\). Circles are inscribed in triangles \(ABM\) and \(CBM\). Find the distance between the points of tangency of these circles with the segment \(BM\).

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