
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 the function $f(x) = (\log_{2}x)^{2}+4\log_{2}x+m$, where $x\in[\frac{1}{8},4]$, and $m$ is a constant.
(I) Assuming the function $f(x)$ has a zero point greater than $1$, find the range of values for the real number $m$;
(II) Assuming the function $f(x)$ has two distinct zero points $\alpha$ and $\beta$, find the range of values for $m$ and the value of $\alpha\cdot\beta$.

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