
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
Is there an infinite sequence of positive terms \(a_{1}, a_{2}, \ldots, a_{n}, \ldots\) such that for every integer \(n \geq 1\),

\[a_{n+2} = a_{n} - a_{n+1}?\]

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