
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:
\[
y = 3x + 4, \quad 4y = 12x + 20, \quad 2y = 6x - 1, \quad 3y = 2x - 6, \quad 5y = -15x + 5.
\]
Determine how many pairs of these lines are either parallel or perpendicular to each other.

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