
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
Define the function $g(x)$ such that:
\[ g(x) = \left\lceil \frac{1}{x+1} \right\rceil \text{ for } x > -1, \]
\[ g(x) = \left\lfloor \frac{1}{x+1} \right\rfloor \text{ for } x < -1. \]
$g(x)$ is not defined at $x = -1$. Which integer is not in the range of $g(x)$?

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