
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 a triangle with known sides \(a = 2\), \(b = 3\), and area \(S = \frac{3 \sqrt{15}}{4}\), the median drawn to its third side is less than half of that side.

Find the radius of the circumcircle of this triangle.

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