
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
Triangle \( ABC \) has \( AB=24 \), \( AC=26 \), and \( BC=22 \). Points \( D \) and \( E \) are located on \( \overline{AB} \) and \( \overline{AC} \), respectively, so that \( \overline{DE} \) is parallel to \( \overline{BC} \) and contains the center of the inscribed circle of triangle \( ABC \). Calculate \( DE \) and express it in the simplest form.

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