
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 factory produces two types of products, A and B, with profits P and Q (in ten thousand yuan), respectively. The relationship between the profits and the invested capital m (in ten thousand yuan) follows the empirical formulas P = (1/3)m + 65 and Q = 76 + 4√m. Now, 150 ten thousand yuan of capital will be invested in producing products A and B, with a minimum investment of 25 ten thousand yuan for each product.

1. Let x represent the capital (in ten thousand yuan) invested in product B. Derive the function y (in ten thousand yuan) representing the total profit in terms of x and determine its domain.
2. How should the capital be allocated to maximize the total profit? What is the maximum profit?

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