
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
Two lines are given by the systems of equations:

$$
\frac{x-x_{1}}{m_{1}}=\frac{y-y_{1}}{n_{1}}=\frac{z-z_{i}}{p_{1}} \quad \text{and} \quad \frac{x-x_{2}}{m_{2}}=\frac{y-y_{2}}{n_{2}}=\frac{z-z_{2}}{p_{2}}
$$

Write the condition for these lines to be parallel. Write the condition for these lines to be perpendicular.

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