
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 certain online store predicted that a fashionable $T$-shirt would sell well. They purchased this type of $T$-shirt for $4000$ yuan and quickly sold out. Then they purchased a second batch of this type of $T$-shirt for $5400$ yuan. The quantity of the second batch of $T$-shirts was $1.5$ times that of the first batch, and the cost price of each $T$-shirt in the second batch was $5$ yuan less than that in the first batch.  
$(1)$ Find the cost price of each $T$-shirt in the first batch.  
$(2)$ If the selling price of the first batch of $T$-shirts is $70$ yuan per piece, and the boss wants the total profit after selling both batches of $T-shirts to be no less than $4060$ yuan, what is the minimum selling price per piece for the second batch of $T-shirts? (The selling price of the $T$-shirt is an integer)

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