
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
A food factory needs to regularly purchase food additives. The factory requires 200 kg of food additives daily, with a price of 1.8 yuan/kg. Each purchase incurs a shipping fee of 236 yuan, and storage fees must be paid for the number of days (N) the additives are stored. The storage fee standards are as follows: within 7 days (inclusive), a flat rate of 10 yuan/day is charged; for days exceeding 7 days, the fee is 0.03 yuan/kg per day based on the remaining weight of the additives.

1. Calculate the storage fee (P) in yuan when the additives are purchased every 9 days.
2. Let x represent the number of days between purchases. Derive the function y(x) representing the factory's total cost in yuan during these x days, and determine the number of days between purchases that minimizes the average daily cost.

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