
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 heaps of stones on the table, it is said that there are  $\textit{many}$  stones on the table, if we can find  $50$  piles and number them with the numbers from  $1$  to  $50$  so that the first pile contains at least one stone, the second - at least two stones,..., the  $50$ -th has at least  $50$  stones. Let the table be initially contain  $100$  piles of  $100$  stones each. Find the largest  $n \leq 10 000$  such that after removing any  $n$  stones, there will still be  $\textit{many}$  stones left on the table.

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