
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 that $[x]$ represents the greatest integer less than or equal to $x$, for example, $[-1.5]=-2$, $[1.5]=1$. Let the function $f(x)=[x[x]]$, when $x\in[0,n)$ ($n\in\mathbb{N}^*$), the range of the function $f(x)$ is the set $A$, then the number of elements in $A$ is \_\_\_\_\_.

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