
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 infinite bounded sequences of natural numbers \( a_{1}, a_{2}, a_{3}, \ldots \) such that for all members starting from the third one, the following is true:

$$
a_{n} = \frac{a_{n-1} + a_{n-2}}{\gcd(a_{n-1}, a_{n-2})}
$$

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