
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 factory spent 20,000 yuan designing a style of clothing. According to experience, the cost of producing 100 sets of this style of clothing is 10,000 yuan. The sales revenue P(x) (in units of 10,000 yuan) for producing x (in hundreds of sets) is given by:

P(x) = $$\begin{cases} -0.4x^{2}+4.2x-0.8，0＜x≤5， \\ 14.7- \frac {9}{x-3}，x＞5\end{cases}$$

1. How many sets of this style of clothing must the factory produce at minimum to avoid a loss?
2. Determine how many sets of this style of clothing the factory should produce to maximize profit, and calculate the maximum profit. (Note: Profit = Sales Revenue - Cost, where Cost = Design Fee + Production Cost)

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