
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 plans to purchase two models of robots, $A$ and $B$, to transport goods. It is known that each $A$ robot transports $10$ tons less per day than each $B$ robot, and the number of $A$ robots needed to transport $540$ tons of goods per day is the same as the number of $B$ robots needed to transport $600$ tons per day.  
$(1)$ Find out how many tons of goods each $A$ robot and each $B$ robot transport per day.  
$(2)$ Each $A$ robot costs $12,000$ yuan, and each $B$ robot costs $20,000$ yuan. The company plans to purchase a total of $30$ robots of types $A$ and $B$, ensuring that the daily amount of goods transported is not less than $2830$ tons and the purchase amount does not exceed $480,000$ yuan. Please find the most cost-effective purchasing plan and the minimum total purchase amount in yuan.

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