
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 of points \( A = \left\{(x, y) \left| (x-3)^2 + (y-4)^2 \leq \left(\frac{5}{2}\right)^2 \right.\right\} \) and \( B = \left\{(x, y) \mid (x-4)^2 + (y-5)^2 > \left(\frac{5}{2}\right)^2 \right\} \), find the number of integer points in the intersection \( A \cap B \).

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