
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 has dimensions 6 units by 8 units. Vertices of triangle $DEF$ are placed such that $D$ lies on the lower side of the rectangle, $E$ on the left side, and $F$ on the top side. The coordinates of $D$, $E$, and $F$ are $(6,0)$, $(0,3)$, and $(4,8)$, respectively. Calculate the area of triangle $DEF$.

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