
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
In a notebook, there are $n$ integers written in descending order $a_{1}>a_{2}>\ldots>a_{n}$ and their sum is 2520. It is known that the $k$-th number $a_{k}$, except for the last one, obtained at $k=n$, is $(k+1)$ times smaller than the sum of all other written numbers. Find the maximum possible number $n$ under these conditions. Find these numbers for the maximum possible $n$.

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