
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 product is purchased at a cost price of $40$ yuan and sold at $50$ yuan, with a total of $500$ units sold. It is known that for every $1$ yuan increase in price, $10$ fewer units will be sold. Within the price range of $50$ to $70$ yuan, what should the selling price be in order to make a profit of $8000$ yuan? And how many units should be purchased at this price?

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