
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
Given that the area of triangle \( \triangle ABC \) is 10, let \( D, E, F \) be points on \( AB, BC, AC \) respectively, different from \( A, B, C \), with \( AD = 2 \) and \( DB = 3 \). If the areas of \( \triangle ABE \) and quadrilateral \( DBEF \) are equal, calculate their area.

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