
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
For a sequence \(a_1, a_2, a_3, \ldots\) of real numbers, it is known that
\[ a_n = a_{n-1} + a_{n+2} \quad \text{for} \ n = 2, 3, 4, \ldots \]
What is the largest number of its consecutive elements that can all be positive?

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