
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
Select three different numbers $a_1$, $a_2$, $a_3$ from the set $\{1, 2, 3, 4, \ldots, 10\}$, satisfying $a_2 - a_1 \geq 2$ and $a_3 - a_2 \geq 3$. Calculate the total number of ways to select such three numbers. (Answer with a number)

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