
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
Consider the following equations of five different lines:
\[
y = 4x + 2, \quad 3y = 9x + 3, \quad 2y = -8x + 10, \quad 3y = 8x + 5, \quad y = -\frac{1}{4}x + 6.
\]
Determine how many pairs of these lines are "good", where a pair of lines is considered "good" if they are either parallel or perpendicular to each other.

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