
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
Calculate the remainder $S$ when $x^{105}$ is divided by $x^2 - 4x + 3$.
A) $\frac{3^{105}(x-1) - (x-2)}{2}$
B) $\frac{3^{105}(x-1) - (x-1)}{2}$
C) $\frac{3^{105}(x-2) - (x-1)}{3}$
D) $\frac{3^{105}(x-1) + (x-2)}{2}$

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