
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 trading company purchases a certain type of fruit at a cost of 20 yuan/kg. Market research reveals that the selling price per unit weight \( p \) (in yuan/kg) in the next 48 days is given by the function
\[
p = \frac{1}{4} t + 30 \quad (1 \leq t \leq 48, t \in \mathbb{Z}),
\]
and the daily sales volume \( y \) (in kg) as a function of time \( t \) (in days) is given by
\[
y = 120 - 2t \quad (1 \leq t \leq 48, t \in \mathbb{Z}).
\]
During the first 30 days of actual sales, the company decides to donate a profit of \( n \) yuan for every kilogram of fruit sold to a "targeted poverty alleviation" cause. It is found that, in these first 30 days, the daily sales profit \( W \) (in yuan) after deducting the donation increases with time \( t \) (in days) only for the first 28 days. Determine the range of values for \( n \).

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