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

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