
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
Given a rectangle A with side lengths $a$ and $b$, if there always exists another rectangle B such that the ratio of the perimeter of rectangle B to rectangle A and the ratio of the area of rectangle B to rectangle A are both equal to $k$, then the minimum value of $k$ is ____.

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