
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
Find the remainder $R$ obtained by dividing $x^{101}$ by $x^2 - 5x + 6$.
A) $(2^{101} - 3^{101})x + (3^{101} - 2 \cdot 2^{101})$
B) $(3^{101} - 2^{101})x + (2^{101} - 2 \cdot 3^{101})$
C) $(2^{101} - 3^{101})x + (2^{101} - 3^{101})$
D) $(3^{101} + 2^{101})x - (2 \cdot 3^{101} - 2^{101})$

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