
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 market survey shows that the sales volume and price of a certain product in the past 50 days are functions of the sales time t(days), and the sales volume approximately satisfies f(t)=−2t+200(1≤t≤50,t∈N). The price for the first 30 days is g(x)=12t+30(1≤t≤30,t∈N), and for the last 20 days is g(t)=45(31≤t≤50,t∈N).
(1) Write out the daily sales S of the product as a function of time t;
(2) Find the maximum value of the daily sales S.

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