
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 $ABC,$ $AB = 7,$ $BC = 8,$ and $AC = 9.$ If $D$ and $E$ are chosen on $\overline{AB}$ and $\overline{AC}$ so that $AD = 3$ and $AE = 6,$ then find the area of triangle $ADE.$

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