
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
Let $k$ be a positive constant, and let a point $P$ have coordinates $(x, y)$ such that $x = ky$. Define $r$ as the distance from the origin to point $P$, and set $s=\frac{y}{r}$ and $c=\frac{x}{r}$. Determine the range of values for $s^2 - c^2$.
**A)** $(-\infty, -1) \cup (1, \infty)$  
**B)** $[-1, 1]$  
**C)** $(-1, 1)$  
**D)** $[-1, 0)$  
**E)** $(0, 1)$

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