
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 sum of the non-negative real numbers \( s_{1}, s_{2}, \ldots, s_{2004} \) is 2. Additionally, we know that 

\[ s_{1} s_{2} + s_{2} s_{3} + \cdots + s_{2003} s_{2004} + s_{2004} s_{1} = 1 \]

Determine the minimum and maximum possible values of the expression 

\[ S = s_{1}^2 + s_{2}^2 + \cdots + s_{2004}^2 \] 

under these conditions.

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