
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 a triangle $DEF$ inscribed in a rectangle with dimensions 3 units by 6 units. The vertices of the triangle are on the sides of the rectangle as follows: $D$ is on the bottom side, $E$ is on the right side, and $F$ is on the top side. Find the area of triangle $DEF$ if $D$ is 1 unit from the left side, $E$ is 2 units from the bottom side, and $F$ is 1 unit from the right side.

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