
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 flower shop buys several roses from a farm every day at a price of 5 yuan per rose and then sells them at a price of 10 yuan per rose. If the roses are not sold by the end of the day, they are discarded as waste.

1. If the shop buys 16 roses in one day, find the function expression of the day's profit $y$ (in yuan) with respect to the day's demand $n$ (in branches, $n \in \mathbf{N}$).

2. The shop recorded the daily demand for roses (in branches) over 100 days and organized the data into Table 1. The frequencies recorded over 100 days are used as the probabilities for the demands.

   (i) If the shop buys 16 roses in one day, let $X$ denote the day's profit (in yuan). Find the probability distribution, expected value, and variance of $X$.

   (ii) If the shop plans to buy 16 or 17 roses in one day, which quantity should it buy? Please provide your reasoning.

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