
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
"Nine years to sharpen a sword, the blade is tested in June." To help with the high school entrance exam and effectively alleviate students' pre-exam pressure, a certain ninth-grade class in a middle school carried out a group expansion activity to reduce stress before the exam. The school prepared a total of 15 small projects in the categories of "energy transfer" and "leaping over the dragon gate." The number of "energy transfer" projects is 3 less than twice the number of "leaping over the dragon gate" projects.<br/>$(1)$ How many projects are there in each category of "energy transfer" and "leaping over the dragon gate"?<br/>$(2)$ The average time for "energy transfer" and "leaping over the dragon gate" projects is 6 minutes and 8 minutes, respectively (ignoring project transition time). Due to time constraints, only 10 projects can be carried out in the actual expansion activity. The number of "leaping over the dragon gate" projects is more than half the number of "energy transfer" projects. How should the activities be designed to minimize the total time spent?

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