
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
Define the function $f(x) = \left\lfloor x \left\lfloor x \right\rfloor \right\rfloor$, where $\left\lfloor x \right\rfloor$ denotes the greatest integer less than or equal to $x$, for example: $\left\lfloor 1.5 \right\rfloor = 1$, $\left\lfloor -1.3 \right\rfloor = -2$. For $x \in [0, n)$ where $n \in \mathbb{N}^*$, let the range of the function $f(x)$ be set $A$, and let the sequence $\{a_n\}$ represent the number of elements in the set $A$. Find an explicit formula for the sequence $\{a_n\}$.

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