
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 certain agricultural and trade group develops animal husbandry and animal husbandry processing industries, with annual profits of $P$ and $Q$ (in ten thousand yuan), respectively. The relationship between these two productions and the invested capital $a$ (in ten thousand yuan) is $P=\frac{a}{3}, Q=\frac{10\sqrt{a}}{3}$. This group plans to invest a total of $60$ ten thousand yuan in these two productions this year. When the maximum profit is obtained, how much will be invested in the animal husbandry industry?

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