
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

Consider the five-digit numbers $\overline{a_{1}a_{2}a_{3}a_{4}a_{5}}$ and $\overline{b_{1}b_{2}b_{3}b_{4}b_{5}}$. The distance between these numbers is defined as the maximum $i$ for which $a_{i} \neq b_{i}$. All five-digit numbers are arranged in some order. What is the minimum possible sum of distances between consecutive numbers in this sequence?

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