
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

Each of the seven dwarfs thought of a positive integer. They all know what numbers the others have thought of. Snow White asked each dwarf what number they thought of.

- The 1st dwarf remained silent.
- The 2nd dwarf said, "My number is equal to the number of the first dwarf."
- The 3rd dwarf said, "My number is equal to the sum of the numbers of the first and second dwarfs."
- The 4th dwarf said, "My number is equal to the sum of the numbers of the first, second, and third dwarfs."

$-\ldots$

- The 7th dwarf said, "My number is equal to the sum of the numbers of the first, second, third, fourth, fifth, and sixth dwarfs."

It is known that the sum of the seven numbers thought of by the dwarfs is 58. It is also known that exactly one dwarf lied. What number could the lying dwarf have thought of? Indicate all possible options.



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