
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
An earthquake occurred in a certain area, and $550$ tents are needed to solve the temporary accommodation problem for the disaster-affected people. Now two factories, A and B, are processing and producing the tents. It is known that the daily processing capacity of factory A is $1.5$ times that of factory B, and factory A takes $4$ days less than factory B to process and produce $240$ tents.

$(1)$ Find out how many tents each factory can process and produce per day.

$(2)$ If the daily processing cost of factory A is $30,000$ yuan and the daily processing cost of factory B is $24,000$ yuan, in order to ensure that the total processing cost of these disaster relief tents does not exceed $600,000$ yuan, how many days should factory A be arranged to process and produce at least?

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