
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
(1) Given the complex number $m^2 - 1 + (m + 1)i$ is a real number, find the value of the real number $m$.
(2) If the complex number $z = (\sqrt{x} - 1) + (x^2 - 3x + 2)i$ corresponds to a point in the second quadrant, determine the range of the real number $x$.

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