
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 lotus root planting pond has a fixed cost of $20,000 per year. The maximum planting capacity per year is 100,000 kilograms. For each additional 10,000 kilograms of lotus roots planted, the cost increases by $10,000. The sales revenue $y$ (in units of $10,000) is related to the quantity of lotus roots planted $x$ (in units of 10,000 kilograms) by the equation $y=-\frac{1}{6}x^3+ax^2+x$ (where $a$ is a constant). If planting 30,000 kilograms of lotus roots results in a profit of $\frac{23}{2}$ million dollars, then to maximize the profit, how many kilograms of lotus roots should be planted each year?

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