
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
Given a triangle \(ABC\), with side lengths \(AB = BC = 78\) and \(AC = 60\).

A circle \(Q_1\) is inscribed in the triangle \(ABC\). Circle \(Q_2\) is tangent to \(Q_1\) and the sides \(AB\) and \(BC\). Circle \(Q_3\) is tangent to \(Q_2\) and also to the sides \(AB\) and \(BC\). Find the radius of circle \(Q_3\).

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