
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 community plans to green the environment by purchasing two types of flowers and grasses, $A$ and $B$, in two phases. In the first phase, $30$ plants of type $A$ and $15$ plants of type $B$ were purchased for a total cost of $675$ yuan. In the second phase, $12$ plants of type $A$ and $5$ plants of type $B$ were purchased. The total cost for both phases was $940$ yuan (the prices of types $A$ and $B$ remained the same in both purchases).  
$(1)$ What is the price per plant for types $A$ and $B$?  
$(2)$ If $31$ plants of types $A$ and $B$ are to be purchased, and the quantity of type $B$ is less than twice the quantity of type $A$, provide a cost-effective plan and calculate the cost for this plan.

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