
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 configuration of four unit squares where each square shares a side with at least one other square, with vertices $A = (1, 2)$ and $B = (2, 1)$ across the diagonal of the central square, and $C = (2, 2)$ a vertex at the top right of this central square. Calculate the area of $\triangle ABC$.

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