
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 \( r_1 \) be the remainder when the polynomial \( x^5 \) is divided by \( x - \frac{1}{2} \), and let \( q_1(x) \) be the respective quotient. Calculate the remainder \( r_2 \) when \( q_1(x) \) is subsequently divided by \( x - 1 \).
A) \( \frac{1}{256} \)  
B) \( -\frac{1}{16} \)  
C) \( 2.9375 \)  
D) \( -16 \)  
E) \( 256 \)

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