
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 shopping mall has a pricing function for a certain product over the next $30$ days. The price $P$ (in yuan) is related to the time $t$ (in days) as follows: $P= \begin{cases} t+30, & 0 < t < 15, t \in \mathbb{N} \\ -t+60, & 15 \leqslant t \leqslant 30, t \in \mathbb{N} \end{cases}$. The daily sales volume of the product is $Q=-t+40$ $(0 < t \leqslant 30, t \in \mathbb{N})$. Find the maximum daily sales revenue for this product and indicate on which day of the $30$ days the daily sales revenue is the highest.

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