
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 shopping mall is celebrating its first anniversary by offering a "discount on discount" promotion: all goods in the mall are sold at 80% of the marked price, and for every 500 yuan spent after the discount, an additional 100 yuan is deducted. If the marked price of a product is 1500 yuan, then the actual payment for the product is $1500 \times 0.8 - 200 = 1000$ (yuan). Let the actual discount rate for purchasing a product be $$\frac {\text{actual payment amount}}{\text{product's marked price}}$$. Suppose the marked price of a product is x yuan, and the actual discount rate obtained for purchasing the product is y.  
(1) Write the function expression of y with respect to x when $x \in (0, 1000]$ and calculate the actual discount rate for a product with a marked price of 1000 yuan;  
(2) For products with a marked price in $[2500, 3500]$, at what marked price will the customer obtain an actual discount rate lower than $\frac {2}{3}$?

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