
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 $XYZ$, where $XY = 8$, $YZ = 12$, and $XZ = 14$. Points $D$ and $E$ are selected on $\overline{XY}$ and $\overline{XZ}$ respectively, such that $XD = 3$ and $XE = 9$. Calculate the area of triangle $XDE$.

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