
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 sales price $P$ (in yuan) of a certain product over the past 30 days as a function of time $t$ (in days) is given by
$$
P = \begin{cases} 
t + 20, & 0 < t < 25, t \in \mathbb{N}^{*} \\ 
-t + 70, & 25 \leq t \leq 30, t \in \mathbb{N}^{*}
\end{cases}
$$
The daily sales volume $Q$ (in units) as a function of time $t$ (in days) is given by $Q = -t + 40$ ($0 < t \leq 30, t \in \mathbb{N}^{*}$).
Find the maximum daily sales revenue of this product and indicate on which day of the 30 days the maximum daily sales revenue occurs.

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