
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
Reading and understanding  
Within the range of rational numbers, we define a new operation "$\oplus$" between three numbers as follows: $a\oplus b\oplus c=\frac{1}{2}\left(|a-b-c|+a+b+c\right)$. For example, $\left(-1\right)\oplus 2\oplus 3=\frac{1}{2}\left[|-1-2-3|+\left(-1\right)+2+3\right]=5$.  
Answer the following questions:  
$(1)$ Calculate the value of $3\oplus \left(-2\right)\oplus \left(-3\right)$;  
$(2)$ Among the 15 numbers $-\frac{6}{7}$, $-\frac{5}{7}$, $-\frac{4}{7}$, ..., $-\frac{1}{7}$, $0$, $\frac{1}{9}$, $\frac{2}{9}$, $\frac{3}{9}$, ..., $\frac{8}{9}$, choose any three numbers as the values of $a$, $b$, $c$, perform the operation "$a\oplus b\oplus c$", and find the maximum value among all the results.

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