
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 \( a_{0}, a_{1}, a_{2}, \ldots \) be a sequence of real numbers defined by \( a_{0}=21 \), \( a_{1}=35 \), and \( a_{n+2}=4 a_{n+1}-4 a_{n}+n^{2} \) for \( n \geq 2 \). Compute the remainder obtained when \( a_{2006} \) is divided by 100.

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