
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
Consider a square with side length $2y$. Inside this square, a smaller square of side $y$ is inscribed such that its sides are parallel to the sides of the larger square. This configuration divides the remaining area into four congruent right triangles. Determine the perimeter of one of these congruent right triangles.

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