
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
With 5 non-zero digits, we can form 120 numbers without repeating any digit in a single number. Let $S$ be the sum of all these numbers. Determine the sum of the digits of $S$, being:

a) 1, 3, 5, 7, and 9 the 5 digits;

b) 0, 2, 4, 6, and 8 the 5 digits, remembering that 02468 is a number with 4 digits and, therefore, we will not have 120 numbers in this case.

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