
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
Determine the number of distinct numbers generated by the list
\[
\left\lfloor \frac{1^2}{500} \right\rfloor, \ \left\lfloor \frac{2^2}{500} \right\rfloor, \ \left\lfloor \frac{3^2}{500} \right\rfloor, \ \dots, \ \left\lfloor \frac{1000^2}{500} \right\rfloor.
\]

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