
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 plane coordinate system $(xOy)$, we define a non-zero vector perpendicular to a line in the plane as the normal vector of the line. Using the method of finding the trajectory equation of a moving point, we can find the equation of the line passing through point $A(-3, 4)$ with normal vector $\overrightarrow{n}=(1,-2)$ to be $1×(x+3)+(-2)×(y-4)=0$, which simplifies to $x-2y+11=0$. By analogy with this method, in the space coordinate system $(O-xyz)$, find the equation of the plane passing through point $A(1, 2, 3)$ with normal vector $\overrightarrow{n}=(-1, -2, 1)$.

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