
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
For a natural number \( n \), let \( S(n) \) denote the sum of its digits. For example, \( S(611) = 6 + 1 + 1 = 8 \). Let \( a, b, \) and \( c \) each be three-digit numbers such that \( a + b + c = 2005 \). Let \( M \) be the maximum value of \( S(a) + S(b) + S(c) \). How many sets of \( (a, b, c) \) satisfy \( S(a) + S(b) + S(c) = M \)?

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