
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
Given the point \((x,y) = \left( \frac{s^2 - 1}{s^2 + 1}, \frac{2s}{s^2 + 1} \right)\) for real numbers $s,$ determine the type of curve that contains all the plotted points.

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