
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
Consider the set \(\{0, 1, 2, \ldots, 12\}\). Determine the number of sets of three distinct digits from this set such that the digits in each set are in an arithmetic sequence and the common difference is even.
A) 17
B) 18
C) 19
D) 20

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