
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
Consider a point $P$ with coordinates $(x, y, z)$ in a 3D space. Let $r$ be the distance from the origin to this point, and define $s = \frac{y}{r}$ and $c = \frac{x}{r}$. Compute the values range of $s^2 - c^2$.
A) less than -1 and greater than +1, both excluded
B) less than -1 and greater than +1, both included
C) between -1 and +1, both excluded
D) between -1 and +1, both included
E) -1 and +1 only

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