
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
Let $m \in \mathbb{R}$. In the Cartesian coordinate system, given vectors $\overrightarrow{a} = (mx, y+1)$ and $\overrightarrow{b} = (x, y-1)$, and $\overrightarrow{a} \perp \overrightarrow{b}$, the trajectory of the moving point $M(x, y)$ is denoted as $E$. The equation of the trajectory $E$ is \_\_\_\_\_\_.

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