
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 wholesaler bought 500 kilograms of a certain type of fruit at a price of 40 yuan per kilogram. According to market forecasts, the selling price $y$ (yuan per kilogram) of this fruit is a function of the storage time $x$ (days), given by $y=60+2x$. However, an average of 10 kilograms of this fruit will be lost each day, and it can be stored for up to 8 days at most. Additionally, the wholesaler needs to spend 40 yuan per day on storage costs.  
(1) If the wholesaler sells all the fruit after storing it for 1 day, the selling price of the fruit at that time will be \_\_\_\_\_\_ (yuan per kilogram), and the total profit obtained will be \_\_\_\_\_\_ (yuan);  
(2) Let the wholesaler sell all the fruit after storing it for $x$ days, try to find the function relationship between the total profit $w$ (yuan) obtained by the wholesaler and the storage time $x$ (days);  
(3) Find the maximum profit that the wholesaler can obtain from operating this batch of fruit.

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