
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
Determine the number of pairs of integers, \((a, b)\), with \(1 \leq a \leq 100\) so that the line with equation \(b=ax-4y\) passes through point \((r, 0)\), where \(r\) is a real number with \(0 \leq r \leq 3\), and passes through point \((s, 4)\), where \(s\) is a real number with \(2 \leq s \leq 4\).

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