
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
After learning about functions, the mathematics team of a high school first grade conducted a mathematical modeling activity. Through a survey of the sales of a certain product in a supermarket near the school, it was found that the relationship between the daily sales price P(x) (in yuan per item) of the product in the past month (calculated as 30 days) and the time x (in days) approximately satisfies the function P(x) = 1 + $\frac{k}{x}$ (where k is a constant, and k > 0). The relationship between the daily sales quantity Q(x) (in items) of the product and the time x (days) is shown in the table below:

| x (days) | 10  | 20  | 25  | 30  |
|----------|-----|-----|-----|-----|
| Q(x) (items) | 110 | 120 | 125 | 120 |

It is known that the daily sales revenue of the product on the 10th day is 121, and the function relationship between the daily sales revenue and x is f(x) (unit: yuan).

(1) Find the value of k.

(2) Provide the following two function models: ① Q(x) = a<sup>x</sup> (a > 0, a ≠ 1), ② Q(x) = a|x-25|+b (a ≠ 0). Based on the data in the table, choose the most suitable function to describe the relationship between the daily sales quantity Q(x) of the product and the time x, and find the analytical expression of that function.

(3) Based on Q(x) in (2), find the minimum value of f(x) (1 ≤ x ≤ 30, x ∈ N*).

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