
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
In the series of activities with the theme "Labor Creates a Better Life" at school, Class 8 (1) is responsible for the design, planting, and maintenance of a green corner on campus. The students agreed that each person would take care of a pot of green plants. They planned to purchase a total of 46 pots of two types of green plants, green lily and spider plant, with the number of green lily pots being at least twice the number of spider plant pots. It is known that each green lily pot costs $9, and each spider plant pot costs $6.
- $(1)$ The purchasing team plans to use the entire budget of $390 to purchase green lilies and spider plants. How many pots of green lilies and spider plants can be purchased?
- $(2)$ The planning team believes that there is a cheaper purchasing plan than $390 and requests the minimum total cost of purchasing the two types of green plants.

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