
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
The right-angled triangle has a base which is 4 times its height. Four such triangles are placed so that their hypotenuses form the boundary of a large square. What is the side length of the shaded square in the diagram?

A) \(2x\)  
B) \(2 \sqrt{2} x\)  
C) \(3x\)  
D) \(2 \sqrt{3} x\)  
E) \(\sqrt{15} x\)

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