
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 where the lengths of the sides are $a$ and $b$. On its diagonal, a triangle with three unequal sides is constructed so that its area equals that of the rectangle. Find the length of the altitude drawn to the base (diagonal).
**A)** $\frac{2a}{\sqrt{a^2 + b^2}}$
**B)** $\frac{2b}{\sqrt{a^2 + b^2}}$
**C)** $\frac{2ab}{\sqrt{a^2 + b^2}}$
**D)** $\frac{ab}{\sqrt{a^2 + b^2}}$
**E)** $\sqrt{a^2 + b^2}$

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