
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
There are 15 cards, each with 3 different Chinese characters. No two cards have the exact same set of Chinese characters, and in any set of 6 cards, there are always at least 2 cards that share a common Chinese character. What is the maximum number of different Chinese characters that can be on these 15 cards?

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