
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
To strengthen cultural confidence and shape the soul of rural revitalization. To develop the tourism economy, a rural enterprise produces a batch of "Beautiful Countryside" themed cultural shirts for sale. The production cost of the first batch of cultural shirts is $3000$ yuan. After being launched, the cultural shirts are in short supply. Another batch of the same cultural shirts is produced for $6600$ yuan. The quantity of the second batch is twice that of the first batch, but due to the increase in raw material prices, the cost of each shirt in the second batch has increased by $3$ yuan.  
$(1)$ What is the cost of each shirt in the first batch produced by the enterprise?  
$(2)$ The two batches of cultural shirts are priced the same. At the end of the season, the last 30 shirts are sold at a 40% discount. What should be the price of each shirt so that the sales profit margin of the two batches of shirts is equal to $50\%$?  
Note: Profit margin $=($Sales amount$-$Cost$)\div $Cost

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