
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
Find all natural numbers \(a, b\) such that the equation \(2ab + 3b = b^2 + 6a + 6\) is satisfied. In the answer, specify \(a\) and \(b\) in this order, separated by a comma or semicolon. From all possible options, if there are several, write the one with the highest sum \(a + b\).

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