
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
A sequence \( s_{0}, s_{1}, s_{2}, s_{3}, \ldots \) is defined by \( s_{0}=s_{1}=1 \) and, for every positive integer \( n \), \( s_{2n}=s_{n} \), \( s_{4n+1}=s_{2n+1} \), and \( s_{4n-1}=s_{2n-1} + \frac{s_{2n-1}^2}{s_{n-1}} \). What is the value of \( s_{1000} \)?

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