
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 circle is tangent to the extensions of two sides \( AB \) and \( AD \) of square \( ABCD \) with side length \( 6 + 2 \sqrt{5} \) cm. From point \( C \), two tangents are drawn to this circle. Find the radius of the circle if the angle between the tangents is \( 36^{\circ} \), and it is known that \( \sin 18^{\circ} = \frac{\sqrt{5} - 1}{4} \).

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