
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]

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# Your action step 2

# Your action step 3

...

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system
A certain company is preparing to launch a product. In the preliminary market research, it was found that:
- ① It will cost 1.8 million yuan to introduce a production assembly line.
- ② The approximate relationship between the production cost Q(x) (in million yuan) and the output x (units) satisfies Q(x) = 5 + $\frac{135}{x+1}$, where x ∈ N* (Note: the production cost Q(x) per unit does not include the cost of introducing the production assembly line).
- ③ The market selling price of each product is 100,000 yuan.
- ④ The maximum annual output can reach 100 units.
  
(1) If the company wants to achieve profitability within one year after launching this product, find the minimum number of units (which can all be sold) of this product that need to be produced.
  
(2) Further investigation revealed that due to the epidemic, only 60 units of this product can be sold in the first year. If the products produced in that year are not sold, causing a backlog, each unsold unit will incur a loss of 10,000 yuan. Determine whether the company can achieve profitability in the first year of production. If profitability is possible, find the output level at which the profit is maximized. If profitability is not possible, explain the reason.

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