
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 \( a_1, a_2, a_3, a_4, a_5 \) be distinct positive integers less than 2021. The number of arrays \( (a_1, a_2, a_3, a_4, a_5) \) that satisfy
\[ 
\left(a_1^2 + a_2^2 + a_3^2 + a_4^2 \right) \left(a_2^2 + a_3^2 + a_4^2 + a_5^2 \right) = \left(a_1 a_2 + a_2 a_3 + a_3 a_4 + a_4 a_5 \right)^2 
\]
is _________.


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