
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
Let \(x_{1}, x_{2}, \ldots, x_{200}\) be natural numbers greater than 2 (not necessarily distinct). In a \(200 \times 200\) table, the numbers are arranged as follows: at the intersection of the \(i\)-th row and the \(k\)-th column, the number \(\log _{x_{k}} \frac{x_{i}}{9}\) is written. Find the smallest possible value of the sum of all the numbers in the table.

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