
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 square with integer side length is cut into 12 squares, all of which have integer side length, and at least 10 of which have area 4. What is the smallest possible value of the length of the side of the original square?

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