
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
Suppose \(p(x) = x^8\) and \(d_1(x) = x + \frac{1}{2}\), and let \(d_2(x) = x - \frac{1}{2}\). \(q_1(x)\) and \(r_1\) are respectively the quotient and remainder when \(p(x)\) is divided by \(d_1(x)\); and \(q_2(x)\) and \(r_2\) are respectively the quotient and remainder when \(q_1(x)\) is divided by \(d_2(x)\). Find the value of \(r_2\).
A) 0
B) \(\frac{1}{256}\)
C) \(-\frac{1}{16}\)
D) 256

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