
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 \( ABC \) be a triangle with \( AB = 5 \), \( AC = 4 \), \( BC = 6 \). The angle bisector of \( \angle C \) intersects side \( AB \) at \( X \). Points \( M \) and \( N \) are drawn on sides \( BC \) and \( AC \), respectively, such that \( \overline{XM} \parallel \overline{AC} \) and \( \overline{XN} \parallel \overline{BC} \). Compute the length \( MN \).

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