
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 lines:
\[
y = 3x + 4, \quad 2y = 2x + 6, \quad 3y = 9x - 1, \quad y = -\frac{1}{3}x + 5, \quad 4y = -12x + 3.
\]
Let's say a pair of lines is $\emph{good}$ if the two lines are either parallel or perpendicular to each other. Among all the pairs of lines shown, how many pairs are good?

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