
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 an island, there are two types of people. The truth-tellers always tell the truth, while the liars always lie. Ten islanders have been assigned the numbers $1, 2, \ldots, 10$. Each person received a unique number. Then, each person was asked the following three questions: "Is your number even?", "Is your number divisible by 4?", and "Is your number divisible by 5?". Three people answered "yes" to the first question, six people answered "yes" to the second question, and two people answered "yes" to the third question. Which numbers do the liars have?

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