
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 $f(x) = \left\lceil \dfrac{1}{x+1} \right\rceil$ for $x > 0$, and $f(x) = \left\lceil \dfrac{1}{x-1} \right\rceil$ for $x < 0$. ($f(x)$ is not defined at $x = 0$). Which integer is not in the range of $f(x)$?

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