
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
We will call two numbers almost equal if they are either equal to each other or differ from each other by no more than one unit. A grid rectangle with sides equal to the natural numbers \(a\) and \(b\) is such that it is impossible to cut out a rectangle along the grid lines that has an area almost equal to half of the original rectangle. What is the smallest value that the number \( |a-b| \) can take?

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