
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
Assume a square $ABCD$ where $A$ is at $(0,0)$, $B$ is at $(2,0)$, $C$ is at $(2,2)$, and $D$ is at $(0,2)$. Let $F$ be a point on side $AB$ such that $BF = 1$. If $\triangle BCF$ is a right triangle with $BF$ as one leg and $CF$ as the hypotenuse, find the area of square $ABCD$.
A) 2
B) 4
C) 5
D) 8

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