
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 we replace the two middle digits $\overline{00}$ in 2009 with the two-digit numbers $\overline{ab}$ and $c\bar{d}$ respectively, we obtain perfect squares: $\overline{2ab9}=n^{2}$ and $\overline{2cd9}=m^{2}$, where $m > n$ and $m, n \in \mathbb{N}$. Determine the array $(m+n, \overline{ab}+\overline{cd})$.

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