
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
Twenty-five of the numbers  $1, 2, \cdots , 50$  are chosen. Twenty-five of the numbers $ 51, 52, \cdots, 100$  are also chosen. No two chosen numbers differ by  $0$  or  $50$ . Find the sum of all  $50$  chosen numbers.

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