
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 real number $x$ satisfies the inequality: $x^2 - 4ax + 3a^2 < 0$, and $x = (\frac{1}{2})^{m-1}$, where $m \in (1, 2)$.

(I) If $a = \frac{1}{4}$, and both conditions are true, find the range of values for the real number $x$.

(II) If the latter condition is a sufficient but not necessary condition for the former, find the range of values for the real number $a$.

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