
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
What is the value of $\text{rem}\left(\tfrac{5}{7}, -\tfrac{3}{11}\right)?$ Define the remainder for all real numbers $x$ and $y$ with $y \neq 0$ by \[\text{rem} (x ,y)=x-y\left \lfloor \frac{x}{y} \right \rfloor\] where $\left \lfloor \tfrac{x}{y} \right \rfloor$ denotes the greatest integer less than or equal to $\tfrac{x}{y}$.
A) $-\frac{8}{77}$
B) $-\frac{7}{55}$
C) $\frac{8}{77}$
D) $0$

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