
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 is called a "convex number" if, starting from the first digit (the highest place) up to a certain digit in the middle, the digits are increasingly large, and from this digit to the last digit (the units place), the digits are increasingly small (for example, 1357642 is a "convex number", while 7531 and 1357462 are not "convex numbers"). How many nine-digit "convex numbers" can be formed using the digits 1-9 exactly once?

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