
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
In triangle \( \triangle ABC \), \( BC = 5 \), \( AC = 12 \), \(\angle B = 13^\circ\). On the segments \( AB \) and \( AC \), points \( D \) and \( E \) are chosen respectively, such that the segment \( DE \) divides \( \triangle ABC \) into two regions of equal area. Find the minimum length of such a segment \( DE \).

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