
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 + 1, \\
y &= -5x - 2, \\
y &= 4x + 3, \\
y &= \frac{1}{5}x + 4, \\
y &= -5x + 1.
\end{align*}
Let's say that a pair of lines is $\emph{good}$ if the two lines are either parallel or perpendicular to each other. Among all the pairs of lines shown, how many pairs are good?

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