
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 \( p_1(x) \) and \( s_1 \) are the quotient and remainder, respectively, when the polynomial \( x^9 \) is divided by \( x - \tfrac{1}{3} \), and if \( p_2(x) \) and \( s_2 \) are the quotient and remainder, respectively, when \( p_1(x) \) is divided by \( x - \tfrac{1}{3} \), then what is \( s_2 \)?
A) \( \tfrac{1}{19683} \)
B) \( \tfrac{1}{39366} \)
C) \( \tfrac{1}{2} \)
D) \( -\tfrac{1}{3} \)

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