
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
Sérgio chooses two positive integers \(a\) and \(b\). He writes 4 numbers in his notebook: \(a\), \(a+2\), \(b\), and \(b+2\). Then, all 6 products of two of these numbers are written on the board. Let \(Q\) be the number of perfect squares written on the board. Determine the maximum value of \(Q\).

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