
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 are given any 100 such coins with a total value of 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 \(C\).

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