
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
One side of a rectangle is $1 \mathrm{~cm}$. It is divided into four smaller rectangles by two perpendicular lines, such that the areas of three of the smaller rectangles are not less than $1 \mathrm{~cm}^{2}$, and the area of the fourth rectangle is not less than $2 \mathrm{~cm}^{2}$. What is the minimum length of the other side of the original rectangle?

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