
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
In the set $\{x \in \mathbb{N}^* | x \leq 10\}$, three different numbers $a$, $b$, and $c$ are chosen. How many arithmetic sequences $a$, $b$, $c$ satisfy $12 \leq a + b + c \leq 30$?

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