
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
The function $\lceil x \rceil$ is defined as the smallest integer greater than or equal to $x$. For example, $\lceil 5.67 \rceil = 6$, $\lceil -\tfrac 14 \rceil = 0$, and $\lceil 8 \rceil = 8$.

What is the range of the function $$g(x) = \lceil x \rceil - x~?$$ Express your answer in interval notation.

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