
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 construction team undertakes a 1500-meter road greening project. There are two greening plans during construction: Plan A requires 2 stems of type $A$ flowers and 3 stems of type $B$ flowers to green 1 meter of road, costing 22 yuan; Plan B requires 1 stem of type $A$ flowers and 5 stems of type $B$ flowers to green 1 meter of road, costing 25 yuan. It is required that the total length of road greened according to Plan B should not be less than twice the total length of road greened according to Plan A.

$(1)$ Find the cost per stem of type $A$ and type $B$ flowers, respectively.

$(2)$ Find the total cost of the project when the total length of road greened according to Plan A is how many meters to minimize the total cost of the project? What is the minimum total cost?

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