
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
According to the statistics of a clothing store, for every 3% increase in the price of clothing, the number of pieces sold decreases by 2%. Suppose the price of a certain type of clothing is increased by x%, resulting in the daily operating income (price × number of pieces sold) being y times the original.  
(1) Write the function relationship between y and x;  
(2) To ensure that the operating income does not decrease, within what range should x be controlled?  
(3) What value of x maximizes the operating income?

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