
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 shopping mall sells a desk lamp with a purchase price of 30 yuan for 40 yuan. On average, 600 lamps are sold each month. A survey shows that for every 1 yuan increase in the selling price of this lamp, the sales volume will decrease by 10 units. In order to achieve an average monthly sales profit of 10,000 yuan, the shopping mall decides to adjust the price to increase sales volume and reduce inventory. What should be the selling price of this lamp, and how many lamps should be purchased?

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