
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 \( 1-\frac{9}{x}+\frac{9}{x^2}=0 \), then \( \frac{3}{x} \) equals
A) \( \frac{3}{2} \)
B) \( \frac{3+\sqrt{5}}{2} \)
C) \( \frac{3-\sqrt{5}}{2} \)
D) \( \frac{3-\sqrt{5}}{2} \text{ or } \frac{3+\sqrt{5}}{2} \)
E) \( \frac{6 - 2\sqrt{5}}{4} \text{ or } \frac{6 + 2\sqrt{5}}{4} \)

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