
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 triangle \(XYZ\) and a circle \(\omega\) of radius 2 are given in a plane, such that \(\omega\) intersects segment \(\overline{XY}\) at the points \(A, B\), segment \(\overline{YZ}\) at the points \(C, D\), and segment \(\overline{ZX}\) at the points \(E, F\). Suppose that \(XB > XA\), \(YD > YC\), and \(ZF > ZE\). In addition, \(XA = 1\), \(YC = 2\), \(ZE = 3\), and \(AB = CD = EF\). Compute \(AB\).

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