
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 $\lfloor x\rfloor$ is defined as the largest integer less than or equal to $x$. Consider a function defined by $$f(x) = \lfloor x \rfloor - 2x$$.
What is the range of $f(x)$? Express your answer in interval notation.

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