
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 function that describes the selling price $P$ (in yuan) of a certain product over the recent 30 days as a function of time $t$ (in days) is given by:
$$
P=
\begin{cases}
t+20, & \text{for } 0 < t < 25, \; t \in \mathbb{N}^{+} \\
-t+100, & \text{for } 25 \leq t \le 30, \; t \in \mathbb{N}^{+}
\end{cases}
$$
The daily sales volume $Q$ (in pieces) of this product as a function of time $t$ (in days) is given by: $Q = -t + 40$ (for $0 < t \le 30$, $t \in \mathbb{N}^{*}$). Find the maximum daily sales revenue for this product.

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