
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 \( x \). Given this, calculate the range of the function
$$f(x) = \lfloor 2x\rfloor - 2x.$$
Express your range in interval notation.

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