
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
In the decimal notation of the six-digit number \(a\), there are no zeros and the sum of its digits is 18. Find the sum of all the different numbers obtained by cyclic permutations of its digits. In a cyclic permutation, all digits of the number, except the last one, are shifted one place to the right, and the last digit is moved to the first place.

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