
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 country responded to the call of the World Health Organization (WHO) by issuing the "Guidelines for Physical Exercise and Sedentary Behavior," focusing on reducing sedentary time, strengthening physical exercise, and improving physical condition. It was proposed to engage in moderate-intensity aerobic exercise for at least 150 to 300 minutes per week or vigorous exercise for 75 to 150 minutes. A school held a jumping competition with the following rules: assuming each participant needs to perform 2 or more three-week jumps during the competition. The success rate of person A's three-week jump is 0.7. Upon successful completion, they receive 8 points, and if they fail, they get 4 points. Person A's success rate for a four-week jump is 0.3. Upon successful completion, they receive 15 points, and if they fail, they get 6 points (the success of each jump is independent of each other). 

$(1)$ If person A chooses to perform a three-week jump first and then a four-week jump, find the probability that person A's score exceeds 14 points. 

$(2)$ If person A chooses to perform two consecutive three-week jumps, let $Y$ represent person A's final score. Find the expected value of the random variable $Y$.

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