
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
From the numbers \(1, 2, 3, \cdots, 14\), select \(a_{1}, a_{2}, a_{3}\) in ascending order, such that \(a_{2} - a_{1} \geqslant 3\) and \(a_{3} - a_{2} \geqslant 3\). How many distinct ways can this be done?

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