
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 length $a$ and width $b$. On the diagonal as base, a triangle with three unequal sides is constructed so that its area equals that of the rectangle. Calculate the length of the altitude drawn to the base.

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