
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 per-unit selling price $P$ (in yuan) over the past $30$ days is a function of time $t$ (in days) as follows: $P = \begin{cases} t+20 & 0 < t < 25, t \in \mathbb{N}_+ \\ -t+100 & 25 \leq t \leq 30, t \in \mathbb{N}_+ \end{cases}$. The daily sales volume $Q$ (in units) of this product is a function of time $t$ (in days) as follows: $Q = -t + 40$ $(0 < t \leq 30, t \in \mathbb{N}^*)$. Calculate the maximum daily sales revenue for this product.

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