
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 that each participant needs to perform 2 or more triple jumps during the competition, with a success rate of 0.7 for triple jumps, scoring 8 points for a successful attempt and 4 points for a failed attempt; and a success rate of 0.3 for quadruple jumps, scoring 15 points for a successful attempt and 6 points for a failed attempt (the success of each jump is independent of the others). 

$(1)$ If a participant chooses to perform a triple jump first and then a quadruple jump, find the probability that the participant's score exceeds 14 points. 

$(2)$ If the participant chooses to perform two consecutive triple jumps, let $Y$ represent the participant'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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