
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
Triangle $DEF$ has its vertices $D$, $E$, and $F$ on the sides of a rectangle 6 units by 4 units as shown. Calculate the area of triangle $DEF$. 
- Vertex $D$ is at (0,2), vertex $E$ is at (6,0), and vertex $F$ is at (3,4).

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