
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 triangle \(ABC\), \(AB = 8\), \(BC = 10\), and \(AC = 12\). If \(D\) and \(E\) are chosen on \(\overline{AB}\) and \(\overline{AC}\) respectively so that \(AD = 3\) and \(AE = 8\), then find the area of triangle \(ADE\).

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