
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
Suppose in triangle $\Delta ABC$, $D$ is the foot of the altitude from $A$ to $BC$, and $D$ divides $\Delta ABC$ into two 45-45-90 triangles. If $AD = \sqrt{2}$ centimeters, determine the number of square centimeters in the area of $\Delta ABC$.

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