
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
In 2016, a factory planned to produce a certain product. It is known that the relationship between the total production cost $y$ (in ten thousand yuan) and the total output $x$ (in tons) can be represented by the equation $y = \frac{x^{2}}{10} - 2x + 90$.
(1) When $x = 40$, determine the production cost per ton of the product;
(2) If the factory price per ton of the product is 6 ten thousand yuan, calculate the maximum profit the factory could achieve in 2016.

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