
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
Determine $r_2$ if $q_1(x)$ and $r_1$ are the quotient and remainder, respectively, when the polynomial $x^6$ is divided by $x - \tfrac{1}{3}$, and $q_2(x)$ and $r_2$ are the quotient and remainder, respectively, when $q_1(x)$ is divided by $x - \tfrac{1}{3}$.

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