
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 certain medicine can only be effective in treating a patient when its concentration in the patient's blood is not less than $2g$. It is known that for each intake of $m (1\leq m\leq 4)$ units of the medicine, the function relationship between the concentration $y$ (units: $g$) of the medicine in the blood and time $x$ (units: $h$) is approximately given by $y=mf(x)$, where $f(x)=\left\{\begin{array}{l}\frac{10}{4+x},(0≤x＜4)\\ 4-\frac{x}{2},(4≤x≤6)\end{array}\right.$.<br/>$(1)$ If a patient takes $2$ units of the medicine at once, find the duration of effective treatment;<br/>$(2)$ If a patient takes $2$ units of the medicine for the first time, and then takes $n$ units of the medicine after $4h$, in order to maintain effective treatment for the next $2h$, find the minimum value of $n$.

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