
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 \(p_1(x)\) be the quotient and \(s_1\) be the remainder when the polynomial \(x^6\) is divided by \(x - \frac{1}{2}\). Let \(p_2(x)\) be the quotient and \(s_2\) be the remainder when \(p_1(x)\) is divided by \(x - \frac{1}{2}\). Calculate \(s_2\).

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