
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
For a plane region \(D\), let \(N(D)\) denote the number of lattice points in \(D\). Let \(A\) represent the region enclosed by the curve \(y=x^2\) (for \(x \leq 0\)) and the lines \(x=-10\) and \(y=1\) (including the boundaries). Let \(B\) represent the region enclosed by the curve \(y=x^2\) (for \(x \geq 0\)) and the lines \(x=1\) and \(y=100\) (including the boundaries). Find the value of \(N(A \cup B) + N(A \cap B)\).

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