
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 certain product's selling price per unit $p$ (in yuan) as a function of time $t$ (in days) over the recent 30 days is given by 
$$
p= 
\begin{cases} 
t+20, & \text{for } 0<t<25, t\in \mathbb{N} \\
-t+100, & \text{for } 25\leq t\leq 30, t\in \mathbb{N}
\end{cases}
$$
The product's daily sales volume $Q$ (in units) as a function of time $t$ (in days) is $Q=-t+40$ for $0<t\leq30, t\in\mathbb{N}$.  
1. Find the analytical expression for the daily sales revenue of this product.
2. Determine the maximum value of the daily sales revenue and indicate on which day, within the 30 day period, this maximum occurs.

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