
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 maximum distance between the numbers \( a_{1}a_{2}a_{3}a_{4}a_{5} \) and \( b_{1}b_{2}b_{3}b_{4}b_{5} \) is defined as the maximum \( i \) such that \( a_{i} \neq b_{i} \). All five-digit numbers are listed one after another in some order. What is the minimum possible sum of the distances between neighboring numbers?

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