
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
A sheet of paper is divided into squares with a side length of 1. Ivan cut a rectangle along the grid lines and calculated its area and perimeter. Tanya took the scissors from him, saying, "Look, a trick!" She cut a square from the edge of the rectangle along the grid lines, discarded the square, and announced: "Now the remaining shape has the same perimeter as the area of the original rectangle and the same area as the original perimeter!" Ivan confirmed that Tanya was right.

a) What size square did Tanya cut out and discard?

b) Provide an example of such a rectangle and such a square.

c) What were the dimensions of the rectangle that Ivan cut out?

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