
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 rectangle with dimensions 6 units by 7 units. A triangle is formed with its vertices on the sides of the rectangle. Vertex $A$ is on the left side, 3 units from the bottom. Vertex $B$ is on the bottom side, 5 units from the left. Vertex $C$ is on the top side, 2 units from the right. Calculate the area of triangle $ABC$.

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