
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 rectangle with sides of lengths $a$ and $b$, a triangle with three unequal sides is constructed such that its base is the diagonal of the rectangle and its area is twice that of the rectangle. What is the length of the altitude of the triangle to this diagonal?
A) $\frac{2ab}{\sqrt{a^2 + b^2}}$
B) $\frac{4ab}{\sqrt{a^2 + b^2}}$
C) $\frac{ab}{\sqrt{a^2 + b^2}}$
D) $2\sqrt{a^2 + b^2}$

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