
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
A group of adventurers displays their loot. It is known that exactly 9 adventurers have rubies; exactly 8 have emeralds; exactly 2 have sapphires; exactly 11 have diamonds. Additionally, it is known that:

- If an adventurer has diamonds, they either have rubies or sapphires (but not both simultaneously);
- If an adventurer has rubies, they either have emeralds or diamonds (but not both simultaneously).

What is the minimum number of adventurers that could be in this group?

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