
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
Determine the number of all positive ten-digit numbers with the following properties:

- The number includes each of the digits 0, 1, 2, ..., 8, and 9 exactly once.
- Each digit, except for 9, has a neighboring digit that is greater than itself.

(Note: For example, in the number 1230, the digits 1 and 3 are neighboring digits of 2, and the digits 2 and 0 are neighboring digits of 3. The digits 1 and 0 each have only one neighboring digit.)

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