
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 lines $l\_1$: $A\_1x+B\_1y=1$ and $l\_2$: $A\_2x+B\_2y=1$ intersect at point $P(2,3)$, derive the equation of the line passing through points $P\_1(A\_1,B\_1)$ and $P\_2(A\_2,B\_2)$.

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