
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
Write the equation of the line passing through the point \((3, -2, 1)\) and perpendicular to the lines given by the following systems:

$$
\frac{x-1}{2} = \frac{y+2}{3} = \frac{z-3}{-1}
$$

and

$$
\frac{x+3}{4} = \frac{y+1}{-1} = \frac{z+3}{3}
$$

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