
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
The profits obtained from selling two types of products, A and B, are P (in ten thousand yuan) and Q (in ten thousand yuan), respectively. Their relationship with the invested capital t (in ten thousand yuan) follows the empirical formulas $P=3\sqrt{t}$ and $Q=t$. Now, 3 million yuan is invested in managing products A and B, with x million yuan invested in product A. Find:  
(1) The expression of the total profit y (in ten thousand yuan) from managing products A and B as a function of x;  
(2) How should the funds be allocated to products A and B to maximize the total profit y, and what is the maximum value?

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