
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
Given the sequence $\left\{a_{n}\right\}$ where $a_{1}=1, a_{2}=4, a_{3}=10$, and for any $n \geq 2$, the relation $a_{n+1}^{2} - 2 a_{n}^{2} = a_{n} a_{n+2} - 2 a_{n-1} a_{n+1}$ holds, determine the units digit of $a_{21}$.

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