
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 children's department store purchased a batch of Type M clothing, which was priced at 75 yuan/piece for sale, and could still make a 50% profit when sold at a 20% discount. The store has now decided to launch a promotional campaign for Type M clothing, selling each piece at a discount of x yuan on top of the 20% discount, with the daily sales volume y (pieces) and the price reduction of x yuan having the function relationship of $y = 20 + 4x$ ($x > 0$).  
(1) Find the cost price of Type M clothing. (3 points)  
(2) Find the maximum profit $W$ that can be obtained from selling Type M clothing during the promotional period each day. (5 points)

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