
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 $g(x) = \left\lceil \frac{\cos(x)}{x + 3} \right\rceil$ for $x > -3$, and $g(x) = \left\lfloor \frac{\cos(x)}{x + 3} \right\rfloor$ for $x < -3$. ($g(x)$ is not defined at $x = -3$.) Determine if there is an integer that is not in the range of $g(x)$.

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