
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 professor's friend has a rectangular garden, half of which he wants to use for a rose garden, surrounding it with a gravel path of constant width. Could you find a general rule that would equally apply to any rectangular garden, regardless of the ratio of its sides? All measurements should be made within the garden, and the only tool available is a rope, which must be at least as long as the garden.

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