
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]


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A factory produces two types of products, A and B, with profits P and Q (in ten thousand dollars) respectively. The relationship between the profits and the invested capital m (in ten thousand dollars) is as follows: $$P= \frac {1}{2}m+60$$ and $$Q=70+6 \sqrt {m}$$. Now, 200 ten thousand dollars of capital will be invested in the production of products A and B, with the requirement that the invested capital for both products A and B should not be less than 25 ten thousand dollars.

(I) Set the capital invested in product B as x (in ten thousand dollars), and find the function relationship of the total profit y (in ten thousand dollars) with respect to x and its domain;

(II) How should the capital be allocated to maximize the total profit, and find the maximum total profit.

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