
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 maximum value of the function $f\left(x\right)=(x^{2}-6x)\sin \left(x-3\right)+x+a\left(x\in \left[0,6\right]\right)$ is $M$, and the minimum value is $m$. If $M+m=8$, then $a=\_\_\_\_\_\_$.

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