
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 square with side length $4r$. On its diagonal, a triangle is constructed such that its area is twice the area of the square. Find the length of the altitude drawn to the base of this triangle.

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