
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
If we select $a_1, a_2, a_3$ from the numbers $1, 2, \cdots, 14$ in increasing order, such that $a_2 - a_1 \geq 3$ and $a_3 - $a_2 \geq 3$, how many different ways can this be done?

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