
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
With the increasingly mature and perfect applications of the Internet, e-commerce has seen rapid development in recent years. A certain e-commerce platform purchases a certain type of T-shirt at a price of $40$ yuan per piece and sells it at a price of $60$ yuan per piece. According to statistics, the sales volume in the week before "Double $11$" (October $30$th to November $5$th) was $500$ pieces. During "Double $11$" (November $6$th to November $12$th), the e-commerce platform conducted discounted sales. Through investigation, it was found that for every $1$ yuan reduction in price of the T-shirt, the weekly sales volume increased by $50$ pieces based on the sales volume in the week before "Double $11$". If the selling price must not be lower than the cost, and according to the regulations of the pricing department, the profit margin should not exceed $30\%$, how should the pricing be determined to maximize profit? And what is the maximum profit? (Profit margin $=\frac{Profit}{Cost}\times 100\%$)

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