
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 $z = a + bi$ (where $a, b$ are real numbers),
(I) If $z^2$ is a pure imaginary number, and $|z + 1| = \sqrt{2}$, find the value of $b$;
(II) If $a \in \{-1, -2, 0, 1\}$ and $b \in \{1, 2, 3\}$, denote the event "the point corresponding to the complex number $z$ in the complex plane lies in the second quadrant" as event A. Calculate the probability of event A.

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