
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 middle school organized an activity called "Caring for Disabled Children, Spreading Warmth with Love." They purchased black and white cultural shirts for a total of $200$ pieces from a clothing wholesale market for $3500$ yuan. The students from the art club hand-painted the shirts and sold them, donating all the profits to the local disabled welfare foundation. The wholesale price and the retail price after hand-painting for each shirt (in yuan per piece) are shown in the table below:

| Item            | Wholesale Price | Retail Price |
|-----------------|-----------------|--------------|
| Black Shirt     | $25             | $50          |
| White Shirt     | $15             | $35          |

$(1)$ How many black and white shirts did the school purchase?  
$(2)$ If all the shirts were sold after hand-painting, how much profit did the school make in total?

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