
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 the right triangle \( \triangle ABC \), it is known that \( \angle ACB = 90^{\circ} \), \( AC = 21 \), and \( BC = 28 \). A square \( ABDE \) is constructed outward on side \( AB \), and the bisector of \( \angle ACB \) intersects \( DE \) at point \( F \). Find the length of segment \( DF \).

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