
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 $a, b \in \mathbb{R}$, and $a^2 + ab + b^2 = 6$, let the maximum and minimum values of $a^2 - ab + b^2$ be $M$ and $m$ respectively. Then, the value of $M - m$ is \_\_\_\_\_\_.

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