
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 \(\triangle ABC\) be a triangle with \(AB=7\), \(BC=1\), and \(CA=4\sqrt{3}\). The angle trisectors of \(C\) intersect \(\overline{AB}\) at \(D\) and \(E\), and lines \(\overline{AC}\) and \(\overline{BC}\) intersect the circumcircle of \(\triangle CDE\) again at \(X\) and \(Y\), respectively. Find the length of \(XY\).

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