
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 &= 3x + 4, \\
y &= 2x + 6, \\
y &= -\frac{1}{3}x + 1, \\
y &= 3x - 2, \\
y &= -\frac{1}{2}x + 3.
\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}
user