
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 set of numbers ${1, 2, 3, ..., 14}$, we select three numbers $a_1, a_2, a_3$ in increasing order such that $a_2 - a_1 \ge 4$ and $a_3 - a_2 \ge 4$. How many different ways can this selection be made? (Answer with a number.)

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