
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 three numbers $a_{1}, a_{2}, a_{3}$ are chosen from the numbers $1,2, \cdots, 14$ in increasing order such that they satisfy the conditions $a_{2} - a_{1} \geqslant 3$ and $a_{3} - a_{2} \geqslant 3$, how many different ways are there to choose such numbers?

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