
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
Let \( x, y, z, w \) be four consecutive vertices of a regular \( A \)-gon. If the length of the line segment \( xy \) is 2 and the area of the quadrilateral \( xyzw \) is \( a + \sqrt{b} \), find the value of \( B = 2^a \cdot 3^b \).

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