
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
Farmer Li Wei plans to wholesale a certain vegetable at a price of $5$ yuan per kilogram. Due to some farmers blindly expanding their planting, the vegetable became unsalable. In order to speed up sales and reduce losses, Li Wei reduced the price twice and sold the vegetable at a price of $3.2$ yuan per kilogram.<br/>$(1)$ Find the average percentage reduction each time;<br/>$(2)$ Xiao Hua plans to purchase 5 tons of the vegetable from Li Wei. Since the quantity is large, Li Wei decides to offer two discount options:<br/>Option 1: Sell at a 10% discount;<br/>Option 2: No discount, but give a cash discount of $200$ yuan per ton.<br/>Which option is more favorable for Xiao Hua, and explain the reason.

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