
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 two intersecting lines $l_1: A_1x + B_1y = 1$ and $l_2: A_2x + B_2y = 1$ at point $P(2, 3)$, find the equation of the line that passes 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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