
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
A rectangle is 6 units by 8 units. Triangle $DEF$ is formed with vertices $D$, $E$, and $F$ located on the boundary of the rectangle such that $D$ is at $(0,2)$, $E$ is at $(6,0)$, and $F$ is at $(3,8)$. Calculate the area of triangle $DEF$ in square units.

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