
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
Given the sets \(A=\left\{(x, y) \mid (x-3)^{2}+(y-4)^{2} \leqslant\left(\frac{5}{2}\right)^{2}\right\}\) and \(B=\left\{(x, y) \mid (x-4)^{2}+(y-5)^{2}>\left(\frac{5}{2}\right)^{2}\right\}\), find the number of lattice points in the set \(A \cap B\).

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