
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 $S=\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$, and let $A = \{a_1, a_2, a_3\}$ be a subset of $S$ such that $a_1 < a_2 < a_3$ and $a_3 - a_2 \leq 6$. Determine the number of possible subsets $A$ that satisfy these conditions.

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