
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
There are six numbers \( ab, a(a+10), a(b+10), b(a+10), b(b+10), (a+10)(b+10) \) for any pair of natural numbers \( a \) and \( b \), where \( a \neq b \). Among them, for certain \( a \) and \( b \), you can find squares of integers. For which \( a \) and \( b \) will the number of squares be maximized?

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