
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 measures 6 units by 7 units. Triangle $ABC$ has vertices $A$, $B$, and $C$ located on the sides of this rectangle as follows: $A$ is at $(0,2)$, $B$ is at $(6,0)$, and $C$ is at $(3,7)$. Determine the area of triangle $ABC$.

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