
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
The letters $P$, $Q$, $R$, and $S$ represent digits in the following arithmetic operations:
\[
\begin{array}{cc}
  & P\ Q \\
+ & R\ P \\
\hline
  & S\ P \\
\end{array}
\]
and
\[
\begin{array}{cc}
  & P\ Q \\
- & R\ P \\
\hline
  & \ \ P \\
\end{array}
\]
Determine the digit represented by $S$.
A) 0
B) 1
C) 5
D) 9
E) None of the above

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