
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 $y=[x]$ is known as the Gaussian function, also called the floor function. For any real number $x$, $[x]$ is the greatest integer not exceeding $x$. Then, the range of the function $y=[x]+1$ for $-0.5<x<2.5$ is.

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