
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 environmentally friendly energy-saving equipment manufacturing company is faced with demand exceeding supply. It is known that the monthly production quantity $x$ (sets) and the selling price per set $y_1$ (in ten thousand yuan) satisfy the relation $y_1 = 150 - \frac{3}{2}x$, with the selling price per set not less than 90 ten thousand yuan. The monthly production quantity $x$ (sets) and the total production cost $y_2$ (in ten thousand yuan) satisfy the relation $y_2 = 600 + 72x$. How many sets should be produced per month to maximize the average profit per set? What is the maximum average profit?

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