
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 machine produces a certain type of product. If it produces a Grade A product, a profit of $50 is made. If it produces a Grade B product, a profit of $30 is made. If it produces a defective product, a loss of $20 is incurred. The probabilities of the machine producing a Grade A product, a Grade B product, and a defective product are 0.6, 0.3, and 0.1, respectively. What is the expected average profit per product produced by this machine?

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