
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
A rectangle has side lengths $a$ and $b$. On a diagonal as base, a triangle with three unequal sides is constructed such that its area equals that of the rectangle. The length of the altitude drawn to the base of this triangle is:
A) $\frac{ab}{\sqrt{a^2 + b^2}}$
B) $\frac{2a}{\sqrt{a + b}}$
C) $\frac{2ab}{\sqrt{a^2 + b^2}}$
D) $\frac{a^2b^2}{\sqrt{a^2 + b^2}}$
E) $\frac{2a + 2b}{\sqrt{a^2 + b^2}}$

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