
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
For the interval $\left[a,b\right]$, we define $b-a$ as the "length" of this interval. Given that $A$ and $B$ are both subsets of the set $\{x\left|\right.-1\leqslant x\leqslant 1\}$, $A=\{x\left|\right.a\leqslant x\leqslant a+1\}$, $B=\left\{{x|b-\frac{3}{2}≤x≤b}\right\}$, then the range of the "length" of the set $A\cap B$ is ______.

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