
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
Given that $q_3(x)$ and $r_3$ are respectively the quotient and remainder when the polynomial $x^{10}$ is divided by $x - 1$, and that $q_4(x)$ and $r_4$ are the quotient and remainder when $q_3(x)$ is further divided by $x - 1$, determine the value of $r_4$.
A) $0$
B) $1$
C) $5$
D) $10$

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