
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 $2a$. Inside the square, a smaller square with side length $b$ is placed in one corner, such that its sides are flush with two sides of the larger square. The remaining area of the large square is divided into four congruent rectangles. Find the perimeter, in units, of one of these four congruent rectangles. Express your answer in terms of $a$.

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