
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
Given the function $f(x)=x \lfloor x \rfloor$, where $\lfloor x \rfloor$ denotes the greatest integer less than or equal to $x$ (the floor function), such as $\lfloor -2.1 \rfloor=-3$, $\lfloor -3 \rfloor=-3$, $\lfloor 2.2 \rfloor=2$. If $x \in [0, n]$ ($n \in \mathbb{N}^*$), then the range of $f(x)$ is ____.

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