
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
Choose four distinct numbers $a_1, a_2, a_3, a_4$ from the set $\{1, 2, 3, \ldots, 14\}$ such that $a_1 < a_2 < a_3 < a_4$ and the inequalities $a_4 \geq a_3 + 4$, $a_3 \geq a_2 + 3$, and $a_2 \geq a_1 + 2$ are satisfied. How many different combinations are there?

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