
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 the set \( P = \{1, 2, 3, \cdots, n\} \) where \( n \geqslant 7 \). Subset \( A \) of \( P \) is defined as \( \left\{a_{1}, a_{2}, a_{3}\right\} \) where \( a_{1} < a_{2} < a_{3} \). If \( a_{3} \geqslant a_{2} + 3 \geqslant a_{1} + 6 \), then subset \( A \) is called a "good subset" of \( P \). Find the number of such good subsets.

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