
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 \( S = \{1, 2, 3, \cdots, 98, 99, 100\} \). If a three-element subset \( A = \{a, b, c\} \) of \( S \) satisfies \( a + b = 3c \), then \( A \) is said to have property \( P \). Find the number of three-element subsets of \( S \) that have property \( P \).

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