
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 \(\left(a_{n}\right)\) be defined by \(a_{1}=3\), \(a_{2}=2\), and for \(n \geqslant 1\), \(a_{n+2}\) is the remainder of the Euclidean division of \(a_{n}+a_{n+1}\) by 100. Compute the remainder of the Euclidean division of:

\[ a_{1}^{2}+a_{2}^{2}+\cdots+a_{2007}^{2} \]

by 8.

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