
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 moving company plans to purchase two models of machines, $A$ and $B$, to transport goods. Each $A$ machine transports $10$ tons less goods per day than each $B$ machine, and the number of days required for each $A$ machine to transport $450$ tons of goods is the same as the number of days required for each $B$ machine to transport $500$ tons of goods.  
$(1)$ Find out how many tons of goods each $A$ machine and each $B$ machine transport per day, respectively.  
$(2)$ Each $A$ machine costs $15,000$ yuan, and each $B$ machine costs $20,000$ yuan. The company plans to purchase a total of $30$ machines of the two types, ensuring that the daily transportation of goods is not less than $2880$ tons and the purchase amount does not exceed $550,000 yuan. Please help the company find the most cost-effective purchasing plan.

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