
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 \( A = \{1,2,3, \ldots, n\} \), and let \(\{a_{1}, a_{2}, a_{3}\}\left(a_{1}<a_{2}<a_{3}\right)\) be a three-element subset of \( A \). If it satisfies \(a_{3} \geq a_{2} + 3 \geq a_{1} + 6\), then \(\{a_{1}, a_{2}, a_{3}\}\) is called a "good subset" of \( A \). Determine the number of "good subsets" of \( A \).

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