
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
The sequence \(a_1, a_2, a_3, \ldots\) of positive integers is determined by its first two members and the rule \( a_{n+2} = \frac{a_{n+1} + a_n}{\text{gcd}(a_n, a_{n+1})} \). For which values of \(a_1\) and \(a_2\) is this sequence bounded?

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