
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 that the intersection point of two lines $a_{1}x+b_{1}y+1=0$ and $a_{2}x+b_{2}y+1=0$ is $P(2,3)$, find the equation of the line passing through points $Q_{1}(a_{1},b_{1})$ and $Q_{2}(a_{2},b_{2})$.

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