
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 lines:
\begin{align*}
y &= 2x + 4 \\
y &= -x + 1 \\
2y &= 6x + 10 \\
y &= -4x + 7 \\
3y &= 3x - 9 \\
\end{align*}
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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