
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 decided to purchase 6 machines to expand its operations for producing a certain piston. There are two types of machines, A and B, with their prices and daily production quantities per machine shown in the table below. After budgeting, the total cost of purchasing the machines should not exceed 34 million dollars.

|          | A    | B    |
|----------|------|------|
| Price (million dollars per machine) | 7    | 5    |
| Daily production quantity per machine (units) | 100  | 60   |

$(1)$ How many purchasing plans can meet the company's requirements?<br/>$(2)$ If the daily production capacity of the 6 machines purchased by the company cannot be less than 380 units, what kind of purchasing plan should be chosen to save money?

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