
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

An isosceles triangle \( ABC \, (\angle C = 90^\circ) \) and a triangle \( DEF \) are positioned such that point \( D \) lies on side \( AB \) and point \( E \) lies on the extension of side \( AB \) beyond point \( A \). Segment \( KL \) is the midline in both triangles, and the area of quadrilateral \( D K L B \) is \( \frac{5}{8} \) of the area of triangle \( ABC \). Find angle \( DEF \).

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