
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
The school cafeteria regularly purchases rice from a grain store at a price of $1500$ yuan per ton. Each purchase of rice requires a transportation and labor fee of $100$ yuan. It is known that the cafeteria needs $1t$ of rice per day, and the storage cost of rice is $2$ yuan per ton per day. Assuming the cafeteria purchases rice on the day it runs out.

$(1)$ How often should the cafeteria purchase rice to minimize the average daily cost?

$(2)$ The grain store offers a discount: a $5\%$ discount on the price of rice for purchases of no less than $20t$ (i.e., $95\%$ of the original price). Can the cafeteria accept this discount offer? Please explain your reasoning.

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