
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  $n$  be a positive integer. Compute, in terms of  $n$ , the number of sequences  $(x_1,\ldots,x_{2n})$  with each  $x_i\in\{0,1,2,3,4\}$  such that  $x_1^2+\dots+x_{2n}^2$  is divisible by  $5$ .

*2020 CCA Math Bonanza Individual Round #13*

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