
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 lines \( A_{1} x + B_{1} y = 1 \) and \( A_{2} x + B_{2} y = 1 \) intersect at point \( P(-7, 9) \), find the equation of the line passing through points \( P_{1}\left(A_{1}, B_{1}\right) \) and \( P_{2}\left(A_{2}, B_{2}\right) \).

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