
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
Quadrilateral \(ABCD\) is inscribed in circle \(\Gamma\). Segments \(AC\) and \(BD\) intersect at \(E\). Circle \(\gamma\) passes through \(E\) and is tangent to \(\Gamma\) at \(A\). Suppose that the circumcircle of triangle \(BCE\) is tangent to \(\gamma\) at \(E\) and is tangent to line \(CD\) at \(C\). Suppose that \(\Gamma\) has a radius of 3 and \(\gamma\) has a radius of 2. Compute \(BD\).

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