
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 of $p$ and $q$ (in ten thousand dollars) respectively. Their relationship with the invested capital $x$ (in ten thousand dollars) is: $p=\frac{1}{5}x$, $q=\frac{3}{5}\sqrt{x}$. Now, with a capital of $3$ (ten thousand dollars) invested in these two types of goods, how should the capital be allocated between A and B to achieve the maximum profit? What is the maximum profit?

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