
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
Triangle $ABC$ has vertices $A$, $B$, and $C$ on the sides of a rectangle 6 units by 9 units. Point $A$ is located at (6,2), point $B$ at (0,9), and point $C$ at (3,0). Calculate the area of triangle $ABC$ in square units.

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