
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

Verify the following equalities, find the patterns in the table, and write down the next two rows of the table.

$$
\begin{aligned}
3^{2}+4^{2} & =5^{2} \\
10^{2}+11^{2}+12^{2} & =13^{2}+14^{2} \\
21^{2}+22^{2}+23^{2}+24^{2} & =25^{2}+26^{2}+27^{2} \\
36^{2}+37^{2}+38^{2}+39^{2}+40^{2} & =41^{2}+42^{2}+43^{2}+44^{2}
\end{aligned}
$$

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