
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 Xin'an, Henan Province, half of the country's cherry production is located. Xin'an is known as the "hometown of Chinese cherries" because of its large production, high quality, and early maturity. A village group sells cherries to the outside world at the original price of $30$ yuan per kilogram. In order to reduce inventory, they decided to reduce the price. After two price reductions, the selling price became $19.2$ yuan per kilogram.  
$(1)$ Find the average percentage reduction in price each time.  
$(2)$ Due to weather conditions, further discounts are offered based on the percentage calculated in $(1)$. Find the selling price after the next price reduction.

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