
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
Given $m\in R$, in the rectangular coordinate system, it is known that vector $\overrightarrow{a}=(mx,y+1)$, vector $\overrightarrow{b}=(x,y-1)$, and $\overrightarrow{a} \perp \overrightarrow{b}$. The trajectory of the moving point $M(x,y)$ is $E$. Find the equation of trajectory $E$.

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