
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
Determine the minimum value of \( \sum_{k=1}^{50} x_{k} \), where the summation is done over all possible positive numbers \( x_{1}, \ldots, x_{50} \) satisfying \( \sum_{k=1}^{50} \frac{1}{x_{k}} = 1 \).

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