
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&=2x+3 \\ 3y&=6x+4 \\ 4y&=12x-3 \\ 5y&=2x-10 \\ 3y&=x-9.
\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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