
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 l₁: 3x - 6y + 1 = 0, l₂: x - my + 2 = 0, l₃: nx + y + 3 = 0, if l₁ is parallel to l₂ and l₁ is perpendicular to l₃, find the value of m - n.

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