
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
An investment company plans to invest in two financial products, \\(A\\) and \\(B\\). Based on market research and forecasts, the profit \\(y_{1}\\) from product \\(A\\) as a function of the investment amount \\(x\\) is \\(y_{1} = 18 - \frac{180}{x + 10}\\), and the profit \\(y_{2}\\) from product \\(B\\) as a function of the investment amount \\(x\\) is \\(y_{2} = \frac{x}{5}\\) (Note: The units of profit and investment amount are in ten thousand yuan).  
\\((1)\\) The company has \\(100\\) ten thousand yuan in funds, all of which are to be invested in products \\(A\\) and \\(B\\), with \\(x\\) ten thousand yuan invested in product \\(A\\). Express the total profit from products \\(A\\) and \\(B\\) as a function of \\(x\\), and state its domain.  
\\((2)\\) Under the condition of \\((1)\\), how should the \\(100\\) ten thousand yuan be allocated to maximize the company's profit? What is the maximum profit in ten thousand yuan?

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