
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 self-employed individual plans to distribute two types of products, A and B. According to a survey, when the investment amount is $x$ (where $x \geq 0$) in ten thousand yuan, the profits obtained from distributing products A and B are $f(x)$ and $g(x)$ in ten thousand yuan, respectively, where $f(x) = a(x - 1) + 2$ ($a > 0$); $g(x) = 6\ln(x + b)$, ($b > 0$). It is known that when the investment amount is zero, the profit is also zero.  
(1) Determine the values of $a$ and $b$;  
(2) If the self-employed individual is ready to invest 5 ten thousand yuan in these two products, please help him devise an investment plan to maximize his profit, and calculate the maximum value of his income. (Round to 0.1, reference data: $\ln 3 \approx 1.10$).

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