
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 $1, 2, \cdots, 14$, select \(a_{1}, a_{2}, a_{3}\) in ascending order such that they satisfy the conditions:
\[
a_{2} - a_{1} \geq 3 \quad \text{and} \quad a_{3} - a_{2} \geq 3
\]
How many different ways are there to make such selections?

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