
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
The remainder \( R \) obtained by dividing \( x^{101} \) by \( x^2-5x+6 \) is a polynomial of degree less than 2. Determine the form of \( R \).
A) \( 3^{101}x - 2x + 2^{101} - 3 \)  
B) \( 3^{101}x - 2^{101}x + 2^{101} - 2\cdot3^{101} \)  
C) \( 3^{102}x - 2^{102} + 2^{101} \)  
D) \( 3^{100}x - 2^{100}x + 3^{101} \)

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