
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 squares of a squared paper are enumerated as shown on the picture. 
\[\begin{array}{|c|c|c|c|c|c}
\ddots &&&&& \hline
10&\ddots&&&& \hline
6&9&\ddots&&& \hline
3&5&8&12&\ddots& \hline
1&2&4&7&11&\ddots \hline
\end{array}\]
Devise a polynomial  $p(m, n)$  in two variables such that for any  $m, n \in \mathbb{N}$  the number written in the square with coordinates  $(m, n)$  is equal to  $p(m, n)$ .

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