
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
Let \(a_{1} = 21\) and \(a_{2} = 90\), and for \(n \geq 3\), let \(a_{n}\) be the last two digits of \(a_{n-1} + a_{n-2}\). What is the remainder of \(a_{1}^{2} + a_{2}^{2} + \cdots + a_{20}^{2}\) when it is divided by 8?

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