
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 \( x > -1 \), and \( f(x) = \left\lfloor\dfrac{1}{x+1}\right\rfloor \) for \( x < -1 \). \( f(x) \) is not defined at \( x = -1 \). Determine which integer is not in the range of \( f(x) \).

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