
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 ten-digit positive integers with the following properties: $\bullet$  Each of the digits  $0, 1, 2, . . . , 8$  and  $9$  is contained exactly once. $\bullet$  Each digit, except  $9$ , has a neighbouring digit that is larger than it.
(Note. For example, in the number  $1230$ , the digits  $1$  and  $3$  are the neighbouring digits of  $2$   while  $2$  and  $0$  are the neighbouring digits of  $3$ . The digits  $1$  and  $0$  have only one neighbouring digit.)

*(Karl Czakler)*

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