
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. Find the point  $D$  on its side  $AC$  and the point  $E$  on its side  $AB$  such that the area of triangle  $ADE$  equals to the area of the quadrilateral  $DEBC$ , and the segment  $DE$  has minimum possible length.

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