
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 $l$ and width $w$. On one of its longer sides, a triangle with three unequal sides is constructed such that its area equals that of the rectangle. Determine the length of the altitude of the triangle drawn to the base, which is the longer side of the rectangle.
A) $w$  
B) $l$  
C) $2w$  
D) $2l$  
E) $w/2$

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