
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
At the beginning of this year, the "Hefei Top 100" mall grandly opened in the Binhu New District. A clothing distributor found that there was a high market demand for a new type of sportswear. The purchase price of the clothing was ¥200 per piece, and the total annual cost for staff salaries and venue rent among other expenses was ¥40,000. After conducting a market survey, it was found that if the selling price was ¥$x$ per piece, then the annual sales volume would be $(800-x)$ pieces.  
$(1)$ Express the annual profit $w$ in an algebraic expression containing $x$;  
Note: Annual profit $=$ (Selling price $-$ Purchase price) $\times$ Annual sales volume $-$ Other expenses  
$(2)$ If the distributor wishes to achieve an annual profit of ¥40,000 for this clothing, and to ensure a higher sales volume, what do you think the selling price should be set at?

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