
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
A square \(ABCD\) is inscribed in a semicircle of radius \(R\) with center at point \(O\) such that points \(A\) and \(D\) lie on the diameter, and points \(B\) and \(C\) lie on the circumference. Find the radius of the circle inscribed in triangle \(OBC\).

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