
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 triangle $ABC$ is formed inside a 6 units by 7 units rectangle. Point $A$ is on the longer side at 2 units from a corner, point $B$ is on the shorter side at 3 units from a corner, and point $C$ is directly at the center of the opposite longer side. Calculate the area of triangle $ABC$ in square units.

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