
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
Consider coins with positive real denominations not exceeding 1. Find the smallest  $C>0$  such that the following holds: if we have any  $100$  such coins with total value  $50$ , then we can always split them into two stacks of  $50$  coins each such that the absolute difference between the total values of the two stacks is at most  $C$ . 

*Merlijn Staps*

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