
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
The necessary and sufficient condition for two lines $A_{1} x + B_{1} y + C_{1} = 0$ and $A_{2} x + B_{2} y + C_{2} = 0$ to be perpendicular is $A_{1} A_{2} - B_{1} B_{2} = 0$.

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