
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
Let the sample space be $\Omega =\{1,2,3,4,5,6,7,8\}$ with equally likely sample points, and events $A=\{1,2,3,4\}$, $B=\{1,2,3,5\}$, $C=\{1,m,n,8\}$, such that $p\left(ABC\right)=p\left(A\right)p\left(B\right)p\left(C\right)$, and satisfying that events $A$, $B$, and $C$ are not pairwise independent. Find $m+n$.

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