
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 $S_n = \frac{1}{2}(c^n + d^n)$ where $c = 4 + 3\sqrt{2}$ and $d = 4 - 3\sqrt{2}$, and $n = 0, 1, 2, \dots,$ compute the units digit of $S_{7890}$.
A) 0
B) 2
C) 4
D) 8
E) 6

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