
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
From the natural numbers between 1 and 99, 50 different numbers were chosen such that no two of them sum to 100 and no two of them sum to 99. Which numbers were chosen?

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