
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 a diagram, given are two right triangles $\triangle ABF$ and $\triangle BDF$ where $B$ is the common vertex. $\triangle ABF$ has side $AB = 8$ units and $BF = 12$ units, and $\triangle BDF$ has side $BD = 8$ units. Point $E$ is on side $AB$ such that $BE:EA = 3:2$. Find the area of $\triangle ADE$.

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