
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
The unit square in the first quadrant of the coordinate plane ($0 \leq x, y \leq 1$) is divided into smaller squares with a side length of $2 \cdot 10^{-4}$. How many nodes of this division (within the unit square) lie on the parabola $y=x^{2}$?

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