
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
Ten natural numbers are written in ascending order such that each number, except the first one, is divisible by one of the preceding numbers. The first number is not 1, and the sum of all 10 numbers is 275. Restore these numbers. 

Let the first number be \( x \), then each of the remaining 9 numbers must be divisible by \( x \), and therefore the sum of all the numbers is also divisible by \( x \). Thus, \( x \) must be a divisor of 275 (\( 275 = 5^2 \cdot 11 \)).

If \( x \) is greater than 5, the smallest possible value of the sum would be \( 11 + 11 \cdot 2 + 11 \cdot 3 + \cdots + 11 \cdot 9 + 11 \cdot 10 = 605 \), which is already greater than 275. Thus, only \( x = 5 \) is suitable. In this case, the minimally possible sum of the numbers is \( 5 + 5 \cdot 2 + 5 \cdot 3 + \cdots + 5 \cdot 9 + 5 \cdot 10 = 275 \).

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