
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
Given a positive integer "specially monotonous" if it is a one-digit number or its digits, when read from left to right, form either a strictly increasing or a strictly decreasing sequence using digits 0 through 7, calculate the total number of specially monotonous integers that are either one-digit or exactly three-digit long.

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