
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
Maggie graphs the six possible lines of the form \( y = mx + b \) where \( m \) is either 1 or -2, and \( b \) is either 0, 1, or 2. For example, one of the lines is \( y = x + 2 \). The lines are all graphed on the same axes. There are exactly \( n \) distinct points, each of which lies on two or more of these lines. What is the value of \( n \)?

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