
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 small business owner plans to distribute two types of products, A and B. According to a survey, when the investment amount is \(x(x\geqslant 0)\) ten thousand dollars, the profits obtained from distributing products A and B are \(f(x)\) and \(g(x)\) ten thousand dollars respectively, where \(f(x)=a(x-1)+2\), \(g(x)=6\ln (x+b)\) (\(a > 0,b > 0\)). It is known that the profit is zero when the investment amount is zero.

(1) Find the values of \(a\) and \(b\);

(2) If this small business owner is prepared to invest 5 ten thousand dollars in these two types of products, please help him devise a fund investment plan so that he can achieve the maximum profit.

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