
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
Consider the statements: 
$\textbf{(1)}\ \text{r and s are both false}\qquad\textbf{(2)}\ \text{r is true and s is false}\qquad\textbf{(3)}\ \text{r is false and s is true}\qquad\textbf{(4)}\ \text{r is true and s is true.}$
How many of these imply the negation of the statement "r and s are both true?"
$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(D)}\ 3\qquad\textbf{(E)}\ 4$

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