
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
If \(q_1(x)\) and \(r_1\) are respectively the quotient and remainder when the polynomial \(x^7\) is divided by \(x - \frac{1}{2}\), and if \(q_2(x)\) and \(r_2\) are the quotient and remainder when \(q_1(x)\) is divided by \(x - \frac{1}{2}\), determine \(r_2\).
A) $\frac{1}{256}$
B) $\frac{7}{64}$
C) $\frac{1}{16}$
D) $-\frac{1}{64}$
E) $-\frac{1}{16}$

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