
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
Suppose  $a_0,a_1,\ldots, a_{2018}$  are integers such that \[(x^2-3x+1)^{1009} = \sum_{k=0}^{2018}a_kx^k\] for all real numbers  $x$ .  Compute the remainder when  $a_0^2 + a_1^2 + \cdots + a_{2018}^2$  is divided by  $2017$ .

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