
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
We know that on the number line, points $M$ and $N$ represent numbers $m$ and $n$ respectively, and the distance between points $M$ and $N$ is $|m-n|$. Given that points $A$, $B$, $C$, and $D$ on the number line represent numbers $a$, $b$, $c$, and $d$ respectively, and $|2a-3c|=|2b-3c|=\frac{2}{3}|d-a|=1(a≠b)$, then the distance between points $B$ and $D$ is ______.

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