
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 price per unit $p($€$)$ of a certain product in the recent $30$ days and its relationship with time $t($day$)$ is given by the function $p= \begin{cases} \overset{t+20,0 < t < 25,t\in N}{-t+100,25\leqslant t\leqslant 30,t\in N} \end{cases}$, and the daily sales volume $Q($unit$)$ of the product and its relationship with time $t($day$)$ is given by the function $Q=-t+40(0 < t\leqslant 30,t\in N)$.
(1) Find the analytical expression for the daily sales of this product;
(2) Find the maximum daily sales and indicate on which day of the $30$ days the daily sales were the highest.

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