
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
Suppose $x$ fulfills the inequalities $\frac{1}{x} \leq 4$ and $\frac{1}{x} \geq -2$. Determine the range of possible values for $x$.
A) $x \geq \frac{1}{4}$\
B) $x > \frac{1}{4}$\
C) $x \leq -\frac{1}{2}$\
D) $x \geq \frac{1}{4} \text{ or } x \leq -\frac{1}{2}$\

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