
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
If there are several piles of stones on the table, it is considered that there are many stones on the table if you can find 50 piles and number them from 1 to 50 such that the first pile has at least one stone, the second one has at least two stones, ..., the fiftieth one has at least fifty stones. Initially, there are 100 piles with 100 stones in each pile on the table. Find the largest $n \leq 10000$ such that after removing any $n$ stones from the initial piles, there will still be many stones on the table. (D. Khramiov)

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