
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 drug must maintain a concentration of at least 2 grams in a patient's bloodstream to be effective. When a patient takes a dose of m (1 ≤ m ≤ 12 and m ∈ R) grams, the concentration y (in grams) of the drug in the bloodstream changes over time x (in hours) according to the function y = $\frac{m}{3}$•f(x), where f(x) = $$\begin{cases} \frac{10}{4 + x}, 0 ≤ x < 6 \\ 4 - \frac{x}{2}, 6 ≤ x ≤ 8 \end{cases}$$.

1. If a patient takes a 9-gram dose, how many hours will the treatment be effective?
2. If a patient takes a 6-gram dose initially and then takes a 3m-gram dose 6 hours later, what is the minimum value of m to ensure continuous effective treatment for the next 2 hours?

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