
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
Due to a traffic accident, a certain liquid on a truck leaked into a pond. In order to decontaminate, following the environmental protection department's suggestion, a chemical agent that reacts with the polluted liquid will be released into the pond. It is known that for every $a$ (where $1 \leq a \leq 4$, $a \in \mathbb{R}$) units of the agent released, the concentration of the agent $y$ (in grams per liter) as a function of time $x$ (in days) is approximately $y = a \cdot f(x)$, where
$$
f(x) = 
\begin{cases} 
\frac {16}{8-x}-1 & \text{for } 0 \le x \le 4 \\
5- \frac {1}{2}x & \text{for } 4 < x \le 10
\end{cases}
$$
If the agent is released multiple times, the concentration of the agent at any given moment is the sum of the concentrations from each release at that moment. According to experience, the concentration of the agent needs to be at least 4 grams per liter to be effective in decontamination.
(1) If 4 units of the agent are released at once, how many days will the decontamination be effective?
(2) If 2 units of the agent are initially released and then $a$ units are released after 6 days, find the minimum value of $a$ in order to maintain effective decontamination for the next 4 days.

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