
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
If $x, y, \sin(z), \text{and } y - \frac{\cos(z)}{x} \neq 0$, evaluate the expression:
\[
\frac{x - \frac{\sin(z)}{y}}{y - \frac{\cos(z)}{x}}
\]
A) $\frac{x}{y}$
B) $\frac{y}{x}$
C) $\frac{x^2y - x \sin(z)}{xy^2 - y \cos(z)}$
D) $\frac{x y \sin(z) - \sin(z) \cos(z)}{x y \cos(z) - \cos^2(z)}$
E) $xy - \frac{1}{xy}$

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