
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
Let $[x]$ denote the greatest integer less than or equal to the real number $x$. Find the number of elements in the set $\left\{n \left|\, n=\left[\frac{k^{2}}{2005}\right], 1 \leqslant k \leqslant 2004, k \in \mathbf{N}\right\}$.

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