
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:
\[
y = 4x + 3, \quad 2y = 8x + 6, \quad 3y = -12x + 2, \quad y = -\frac{1}{4}x + 7, \quad 4y = -x + 4.
\]
Determine the number of pairs of lines that are either parallel or perpendicular.

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