
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 that $x^{120}$ is divided by $x^2-4x+3$, and knowing that the remainder $R$ must be a polynomial of degree less than 2, find the form of $R$.
A) $\frac{(3^{120} - 1)x - (3^{120} + 3)}{2}$
B) $\frac{(3^{120} - 1)x + (3^{120} - 3)}{2}$
C) $\frac{3^{120}(x - 1) - (x - 3)}{2}$
D) $\frac{(3^{120} - 1)x + (3 - 3^{120})}{2}$

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