
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
Solve the following equation in the set of natural numbers:

\[ [a, b] + (a, b) + a + b = a \cdot b \]

(Here, \([a, b]\) denotes the least common multiple of \(a\) and \(b\), while \((a, b)\) denotes the greatest common divisor.)

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