
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 price $f(t)$ (in yuan) over the past $30$ days is related to time $t$ by the following formula: $f(t) = \begin{cases} \frac{1}{3}t + 8, & 0 \leqslant t < 15, t \in \mathbb{N}^{+} \\ -\frac{1}{3}t + 18, & 15 \leqslant t < 30, t \in \mathbb{N}^{+} \end{cases}$, and its sales volume $g(t)$ is related to time $t$ by the formula $g(t)=-t+30, (0 \leqslant t \leqslant 30, t \in \mathbb{N}^{+})$. Determine the maximum daily sales revenue for this product.

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