
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
Given the set $P={a,b,c,d}$ where $a,b,c,d \in {1,2,3,4,5,6,7,8}$, find the probability of the event that satisfies the condition $a+b+c+d=8$. Also, find the expected value of the number of odd elements in the set $P$.

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