
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
The town hall installed a beautiful artwork on the town square. It consists of a certain number of (non-empty) piles of stones, with a total of $\frac{n(n+1)}{2}$ stones. One night, a prankster takes one stone from each pile and creates a new pile. The following night, another prankster does the same, and so on. Will we ever arrive at a stable configuration, meaning a configuration where the number of piles and the number of stones in each pile remains the same?

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