
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
Find the smallest ten-digit natural number, all of whose digits are distinct, such that if all even digits are removed, the remaining digits are 97531, and if all odd digits are removed, the remaining digits are 02468.

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