
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 merchant plans to invest 100,000 yuan in dealing with products A and B. According to market research statistics, when the investment amount is x (0 ≤ x ≤ 10) ten thousand yuan, the revenues obtained from dealing with products A and B are f(x) ten thousand yuan and g(x) ten thousand yuan, respectively. Where f(x) = x + 2, and g(x) is defined as:

$$
g(x) =
\begin{cases}
\frac{10x + 1}{x + 1} & \text{if } 0 \leq x \leq 6 \\
-x^2 + ax - 45 & \text{if } 6 < x \leq 10
\end{cases}
$$

When the merchant invests all 100,000 yuan in dealing with product B, the revenue obtained is 50,000 yuan.

(I) Find the value of the real number a.
(II) If the merchant invests 100,000 yuan in dealing with products A and B, help him formulate a capital investment plan to maximize his total revenue and find the maximum total revenue.

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