
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
Given the value of an item is $C$ dollars, determine the value of $x$ such that after a loss of $x \%$ of the selling price, it is sold for $100$, and it is then sold again with a profit of $x \%$ of the new selling price $S$, where $S$ and $C$ differ by $1 \frac{1}{9}$ dollars.

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