
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 rectangle with a length of $3y$ units and a width of $y$ units. This rectangle is divided into a smaller rectangle of length $x$ units and width $y-x$ units, with four congruent right-angled triangles surrounding it. Find the perimeter of one of the four congruent triangles, and compute the area of the smaller rectangle. Express your answer in terms of $y$.

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