
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 \( A=\{x \mid 5x - a \leqslant 0\} \) and \( B=\{x \mid 6x - b > 0\} \), where \( a, b \in \mathbf{N} \), and \( A \cap B \cap \mathbf{N} = \{2, 3, 4\} \), determine the number of integer pairs \( (a, b) \).

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