
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 \begin{align*}
y &= 4x + 3, \\
2y &= 6x + 2, \\
3y &= 12x - 5, \\
2y &= -3x + 4, \\
4y &= -8x + 7.
\end{align*}
Determine how many pairs of lines are either parallel or perpendicular to each other.

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