
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 $x^ 7 + x^5$ 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 find $s_2$.
A) $\frac{10}{2187}$
B) $0$
C) $\frac{1}{243}$
D) $\frac{1}{2187}$

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