
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
The distance between the numbers \(\overline{a_{1}^{-}} \overline{a_{2}} \overline{a_{2}} \overline{a_{3}} \overline{a_{4}} \overline{a_{4}} \overline{a_{5}}\) and \(\bar{b}_{1} \bar{b} \bar{b} \overline{2} \bar{b} \bar{b} \bar{b} \overline{4} \bar{b}_{5}\) is defined as the largest \(i\) for which \(a_{i} \neq b_{i}\). All five-digit numbers are written one after another in some order. What is the minimal possible sum of the distances between consecutive numbers?

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