
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
Given a square with side length $s$. A triangle is constructed on the diagonal of the square such that its area is half that of the square. Find the length of the altitude drawn to the diagonal.
A) $\frac{s\sqrt{2}}{2}$
B) $s\sqrt{2}$
C) $2s$
D) $s$
E) $2\sqrt{s}$

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