
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 5 units by 4 units. A triangle $ABC$ is formed with vertices on the rectangle's boundary at points $A(0, 1)$, $B(4, 0)$, and $C(3, 5)$. Calculate the area of triangle $ABC$.

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