
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 \( S_n = \frac{1}{2} (x^n + y^n) \) where \( x = 4 + \sqrt{15} \) and \( y = 4 - \sqrt{15} \), and \( n = 5432 \). Determine the units digit of \( S_{5432} \).

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