
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 chose a natural number. They all know the numbers that the others chose. Snow White asked each dwarf what number he chose.

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

$\ldots$

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

It is known that the sum of the seven numbers chosen by the dwarfs is 46. It is also known that exactly one dwarf lied. What number could the lying dwarf have chosen? State all possible options.

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