
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
Through the point $P(1,3)$, a line $l$ is drawn. If $l$ passes through the points $A(a,0)$ and $B(0,b)$, where $a$ and $b$ are both positive integers, determine the number of such lines $l$ that can be drawn.

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