
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 \( S = \{1, 2, 3, 4, \ldots, 50\} \). A 3-element subset \(\{a, b, c\}\) of \(S\) is said to be good if \(a + b + c\) is divisible by 3. Determine the number of 3-element subsets of \(S\) which are good.

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