
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
A pharmaceutical factory is conducting new drug trials in animals. It is known that after administering a dose of $m$ (where $m>0$) of the drug, the concentration $y$ (in milligrams per liter) of the drug released in the animal's body after $x$ hours satisfies the function $y=mf(x)$, where $f(x) = \begin{cases} - \frac {1}{2}x^{2}+2x+8, & 0＜x≤4 \\ - \frac {x}{2}-\log_{2}x+12, & 4＜x≤16\end{cases}$. When the concentration of the drug released in the animal's body is not less than 12 (mg/L), the drug is considered effective.  
(1) To ensure effectiveness within 8 hours (including the 8th hour) from the time of drug administration, find the minimum value of the drug dose $m$ that should be administered;  
(2) If $m=2$ and $k$ is an integer, and the drug remains effective within $k$ hours, find the maximum value of $k$.

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