
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 $\triangle ABC$ has an area of $15$ square units. Points $D$, $E$, and $F$ are on sides $AB$, $BC$, and $CA$ respectively, such that $AD = 3$ and $DB = 2$. If triangle $\triangle ABE$ and quadrilateral $DBEF$ still have equal areas, calculate the area of triangle $\triangle ABE$.

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