
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 that the three numbers $\sqrt{(x-1)^2 + y^2}$, $2$, and $\sqrt{(x+1)^2 + y^2}$ form an arithmetic sequence, where $(x, y)$ corresponds to the curve $C$.
(1) Find the standard equation of $C$;
(2) The straight line $l_1$: $x - y + m = 0$ intersects with the curve $C$ at two distinct points $M$ and $N$, such that $\angle MON$ is an obtuse angle, where $O$ is the origin of the coordinate system. Find the range of $m$.

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