
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
Consider triangle $DEF$ where $D$, $E$, and $F$ are points on the boundary of a rectangle with dimensions 6 units by 3 units. The coordinates of the points are $D(0, 2)$, $E(6, 0)$, and $F(3, 3)$. Calculate the area of triangle $DEF$.

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