
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 of sides $y$ and $z$ units, where a square of side $x$ units is placed touching one of the shorter sides ($y$) of the rectangle. Outside the square, dividing the remaining region into four congruent smaller rectangles. Find the perimeter, in units, of one of the four congruent rectangles with $y$, $z$, and $x$ in the description.

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