
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
Let $A=\{x \mid x^2 - 3x + 2 < 0\}$, $B=\{x \mid \frac{1}{2} < 2^{x-1} < 8\}$, and $C=\{x \mid (x+2)(x-m) < 0\}$, where $m$ is a real number.

(I) Find $A \cap B$;

(II) If $(A \cup B) \subseteq C$, determine the range of values for the real number $m$.

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