
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
In a charity sale event, a class is selling small cakes. When the selling price of each small cake is set at $6, the average number of cakes sold per hour is 30. Little Li found that for every $1 increase in price, the average number of cakes sold per hour decreases by 2, but the price cannot exceed $10.  
$(1)$ If the price of the small cake increases twice based on the original price of $6, and the price after the two increases is $8.64, with the percentage increase being the same each time, what is the percentage increase?  
$(2)$ If the total sales per hour amount to $216, what should be the selling price of the small cake?

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