
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
Let a positive integer \( M \) in base \( n \) be represented such that all its digits are distinct, and each digit (except the leftmost one) differs by \(\pm 1\) from some digit to its left. Find the number of all such positive integers \( M \) in terms of \( n \).

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