
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 trapezoid \(ABCD\) with bases \(AD = 9\) and \(BC = 2\), the angles at bases \(A\) and \(D\) are \(\arctan(4)\) and \(\arctan(2/3)\), respectively. Find the radius of the circle circumscribed around triangle \(CBE\), where \(E\) is the intersection point of the diagonals of the trapezoid.

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