
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 a complex number $z$ satisfying $|z| = \sqrt{2}$, and the imaginary part of $z$ is 1, and the point representing $z$ in the complex plane is located in the second quadrant.  
(1) Find the complex number $z$;  
(2) If $m^2 + m + mz^2$ is a pure imaginary number, find the value of the real number $m$.

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