
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
The 2022 Winter Olympics in Beijing conveyed the spirit of challenging oneself and being positive to the world, guiding a healthy, civilized, and happy way of life. In order to inspire students' interest in sports and promote comprehensive and healthy growth, a certain middle school organized a sports practice activity with the theme "Building Olympic Dreams, Moving Towards the Future" for all students. The students participating in the activity need to randomly select 2 projects from 3 fun projects (jump rope, kicking shuttlecock, basketball shooting) and 2 bouncing projects (high jump, long jump) for competition.  
$(Ⅰ)$ Find the probability that the 2 selected projects are both fun projects.  
$(Ⅱ)$ If one project is selected from fun projects and one from bouncing projects, find the probability that the 2 projects include jump rope but not high jump.

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