
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 park of side length $2$ contains nine potted plants placed at various points either inside or on the boundary of the park. What is the smallest possible distance that can be guaranteed to exist between at least one pair of these plants?

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