
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
The relationship between the selling price $P$ (in yuan) of a certain product within $0$ days and the time $t$ (in days) can be approximated as $P=\begin{cases} t+2, & 1\leqslant t\leqslant 24, t\in N \\ -t+100, & 25\leqslant t\leqslant 30, t\in N \end{cases}$. The daily sales volume $Q$ of the product and the function $t$ (in days) is approximately $Q=-t+40 (1\leqslant t\leqslant 30, t\in N)$. Find the maximum value of $y$, and indicate the day with the largest daily sales.

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