
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 rectangular coordinate system $(Oxyz)$, it is known that a normal vector of plane $(\alpha)$ is $\overrightarrow{n}=(1,-1,2)$, and plane $(\alpha)$ passes through point $A(0,3,1)$. If $P(x,y,z)$ is any point on plane $(\alpha)$, then the equation satisfied by the coordinates of point $P$ is _____.

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