
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
Given that the production cost $C$ (in yuan) of a certain shoe factory per day and the production quantity $n$ (in pairs) have the function relationship $C = 4000 + 50n$.

(1) If the production cost one day is 36,000 yuan, how many pairs of shoes were produced that day?  
(2) If the selling price of each pair of shoes is 90 yuan, and all the produced shoes are sold out, please write down the profit $P$ as a function of the production quantity $n$ for that day, and calculate the minimum number of pairs of shoes that must be produced each day to ensure a daily profit of no less than 8,500 yuan?

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