
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
Under what condition do the three lines given by the equations \( A_{1} x + B_{1} y + C_{1} = 0 \), \( A_{2} x + B_{2} y + C_{2} = 0 \), and \( A_{3} x + B_{3} y + C_{3} = 0 \) pass through the same point?

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