
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 integers among the numbers
$$
\left\lfloor\frac{1^{2}}{2007}\right\rfloor,\left\lfloor\frac{2^{2}}{2007}\right\rfloor, \quad \cdots, \quad \left\lfloor\frac{2007^{2}}{2007}\right\rfloor.
$$

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