
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
Let us call a natural number a "lucky number" if it satisfies the following two conditions:
1. Starting from the third digit, each digit is the difference (larger value minus smaller value) of the two preceding digits.
2. No digit is repeated.

For example, 132, 871, 54132 are "lucky numbers," but 8918 (digit "8" is repeated) and 990 (digit "9" is repeated) are not "lucky numbers." What is the second digit from the left of the largest "lucky number"?

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