
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
Fifty different natural numbers are given, twenty-five of which do not exceed 50, and the remaining ones are greater than 50 but do not exceed 100. Moreover, no two of them differ by exactly 50. Find the sum of these numbers.

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