
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
On a mysterious island, there are two kinds of natives: some always tell the truth (called truth-tellers) and others always lie (called liars). Researchers met several groups of natives and always asked each member of the group how many truth-tellers there are in their group.

- From a four-member group, they received the same number from everyone.
- From another group, they received the numbers $0,1,3,3,3,4$.

How many truth-tellers could be in each group? Determine all possibilities.

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