
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
Define a positive integer as "semi-monotonous" if its digits, when read from left to right, form either a strictly increasing or a strictly decreasing sequence and the number contains at least two distinct digits. Zero can be included but cannot be the leading digit unless followed by another distinct digit. Find the total count of semi-monotonous numbers between 10 and 9876543210 inclusive.

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