
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 supermarket is selling a batch of products and found that the daily sales volume $P$ (in pieces) of this product within 30 days is related to the date $t$ ($1 \leq t \leq 30$, $t \in \mathbb{N}^+$) by the equation $P=kt+b$. It is known that the sales volume on the 5th day was 55 pieces, and on the 10th day was 50 pieces.  
(1) Find the sales volume on the 20th day;  
(2) If the unit price $Q$ (in yuan/piece) is related to $t$ by the formula $$Q= \begin{cases} t+20, & 1\leq t<25 \\ 80-t, & 25\leq t\leq 30 \end{cases} (t \in \mathbb{N}^+),$$ find the maximum daily sales revenue $y$.

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