
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 study group found through a survey of the sales of a certain product in a store during a summer social practice activity that: The relationship between the daily sales price $P(x)$ (in yuan) of the product over the past month (30 days) and time $x$ (in days) approximately satisfies the function $P(x) = 1 + \frac{k}{x}$ (where $k$ is a positive real number). The daily sales quantity $Q(x)$ (in units) of the product with respect to time $x$ (in days) is shown in the table below:

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

It is known that the daily sales revenue of the product on the 10th day is 121 yuan.

1. Find the value of $k$.
2. Given the following two function models: ① $Q(x) = ax + b$, ② $Q(x) = a|x-25| + b$, 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 time $x$, and find the analytical expression of that function.
3. In the case of (2), find the minimum value of the daily sales revenue $f(x)$ of the product ($0 \leq x \leq 30$, $x \in \mathbb{N}^+$).

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