
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]


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A circle with a radius of 15 is tangent to two adjacent sides \( AB \) and \( AD \) of square \( ABCD \). On the other two sides, the circle intercepts segments of 6 and 3 cm from the vertices, respectively. Find the length of the segment that the circle intercepts from vertex \( B \) to the point of tangency.

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