
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 company is organizing a football match for its employees and is preparing to purchase a batch of football equipment. Market research shows that two markets, A and B, are selling the same brand of football team uniforms and footballs at the same price. It is known that each set of uniforms costs $60 more than each football. The cost of three sets of uniforms is equal to the cost of five footballs. After negotiations, Market A offers a deal: for every ten sets of uniforms purchased, one football is given for free; Market B offers a deal: if more than 60 sets of uniforms are purchased, the footballs are sold at an 20% discount.<br/>$(1)$ Find the prices of each set of uniforms and each football.<br/>$(2)$ If 100 sets of uniforms and $y\left(y \gt 10\right)$ footballs are purchased, express the costs of purchasing equipment at Market A and Market B with expressions containing $y$;<br/>$(3)$ Under the conditions in $(2)$, if you are in charge of this purchase task, which market do you think is more cost-effective to buy from?

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