
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]

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[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

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system
A strong acid leak has caused pollution in a river. It is decided to introduce $\text{0.1}$ units of solid alkali into the river, which will gradually dissolve in the water. The concentration of alkali in the water $y$ in relation to time $x$ can be approximately represented as $y= \begin{cases} - \frac {16}{x+2}-x+8\;\;\;\;\;0\leqslant x\leqslant 2 \\ 4-x\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;2 < x\leqslant 4\end{cases}.$ Only when the concentration of alkali in the river is not less than $1$ can an effective inhibition of pollution be achieved.
$(1)$ How long can an effective inhibition of pollution be maintained if only $1$ unit of solid alkali is introduced?
$(2)$ When the concentration of alkali in the river begins to decrease, a second introduction of $1$ unit of solid alkali is made immediately. Thereafter, the concentration of alkali in the river at any time is considered to be the sum of the concentrations of alkali corresponding to each introduction at that time. Find the maximum possible value that the concentration of alkali in the river can reach.

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