
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
Determine the following sums (as functions of $n$):

$$
\begin{aligned}
& A=2^{2}+4^{2}+6^{2}+\ldots+(2n-2)^{2} \\
& B=1^{2}+3^{2}+5^{2}+\ldots+(2n-1)^{2}
\end{aligned}
$$

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