
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
In the Cartesian coordinate system $O-xyz$, find the equation of the plane that passes through the point $P(2, 1, 1)$ and is perpendicular to the line defined by the system of equations $$\begin{cases} x-3y+z+1=0 \\ 3x-2y-2z+1=0 \end{cases}.$$

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