
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 order to better conduct home circuit experiments, Class 1 of Grade 9 of a certain school purchased small electric motors and small light bulbs on an e-commerce platform. It is known that the sum of the price of a small electric motor and a small light bulb on this platform is $12. The students decided to spend $30 on small light bulbs and $45 on small electric motors, with the number of small light bulbs purchased being exactly twice the number of small electric motors.  
$(1)$ Find the price of each small light bulb and small electric motor.  
$(2)$ If Class 1 of Grade 9 decides to purchase a total of 90 small light bulbs and small electric motors, and the number of small light bulbs does not exceed half the number of small electric motors, design a more cost-effective purchasing plan and find the minimum total cost.

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