
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 $x$. Determine the number of distinct elements in the set $\left\{\left[\frac{1^{2}}{2005}\right],\left[\frac{2^{2}}{2005}\right], \ldots,\left[\frac{2005^{2}}{2005}\right]\right\}$.

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