
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 chemical company decided to purchase 10 machines to produce laundry detergent in order to expand its production operations. There are two models of machines, Model A and Model B, available for selection. It is known that Model A costs 60,000 yuan per unit and can produce 15 tons of laundry detergent per day, while Model B costs 40,000 yuan per unit and can produce 10 tons of laundry detergent per day. According to the company's situation, the funds for purchasing machines this time cannot exceed 440,000 yuan.  
$(1)$ How many purchasing plans are available for the company this time? Please calculate and list all the purchasing plans.  
$(2)$ After research, the company requires a daily production capacity of at least 102 tons. Considering cost savings, which purchasing plan should we choose?

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