
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
The teacher has 9 cards, each with a unique number from 1 to 9, and distributes 3 cards to each of three students: A, B, and C. 

A says: The numbers on my three cards form an arithmetic sequence.
B says: The numbers on my three cards form an arithmetic sequence.
C says: The numbers on my three cards do not form an arithmetic sequence.

If all their statements are true, what is the smallest number on the cards that C holds?

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