
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 $M[A]$ denote the number of elements in a non-empty set $A$. Define $|A-B|$ as $$\begin{cases} M[A]-M[B], & \text{if } M[A]\geq M[B] \\ M[B]-M[A], & \text{if } M[A]<M[B] \end{cases}$$ If $A=\{1,2,3\}$, $B=\{x \mid |x^2-2x-3|=a\}$, and $|A-B|=1$, then the range of the real number $a$ is \_\_\_\_\_\_.

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