
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 these five lines:
\begin{align*}
y &= 4x + 3, \\
2y &= 6x + 2, \\
3y &= 12x - 4, \\
2y &= 3x + 1, \\
4y &= -8x + 6.
\end{align*}
Define a pair of lines as $\emph{good}$ if the lines are either parallel, perpendicular, or if one line's slope is exactly double that of another line. How many pairs of lines are good under these conditions?

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