
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 related to time $t$ (in days) with the function $p= \begin{cases} t+20,0 < t < 25,t\in\mathbb{N}^* \\ -t+70,25\leqslant t\leqslant 30,t\in\mathbb{N}^* \end{cases}$. The product's daily sales volume $Q$ (in units) is related to time $t$ (in days) with the function $Q=-t+40(0 < t\leqslant 30,t\in\mathbb{N}^*)$. Determine the maximum daily sales revenue for this product, and identify which of the $30$ days had the maximum daily sales revenue.

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