
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
There are two types of goods, A and B, with profits from operating and selling these goods being M and N million yuan, respectively. Their relationship with the invested capital x million yuan is given by the empirical formulas: M = x/4, N = (3/4)√(x-1) (x ≥ 1). Now, 8 million yuan of capital is invested in operating goods A and B, with at least 1 million yuan required to be invested in good B. To achieve the maximum profit, how much capital should be invested in goods A and B, respectively? What is the maximum profit that can be attained?

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