
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
A positive integer \( n \) is friendly if every pair of neighboring digits of \( n \), written in base 10, differs by exactly 1. For example, 6787 is friendly, but 211 and 901 are not.

Find all odd natural numbers \( m \) for which there exists a friendly integer divisible by \( 64m \).

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