
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 points $A$ and $B$ are on the rays $l_1: y = x$ $(x \geqslant 0)$ and $l_2: y = -x$ $(x \geqslant 0)$ respectively, with $O$ being the origin, and the area of $\triangle OAB$ is a constant value of $2$, find the equation of the trajectory of the midpoint $M$ of segment $AB$.

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