
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
Suppose the remainder for all real numbers $x$ and $y$ (with $y \neq 0$) is defined as \(\text{rem}(x, y)=x-y\left \lfloor \frac{x}{y} \right \rfloor\). Determine the value of \(\text{rem}\left(\frac{5}{6}, -\frac{3}{4}\right)\).
A) $-\frac{5}{12}$
B) $-\frac{7}{9}$
C) $-\frac{2}{3}$
D) $-\frac{1}{4}$
E) $0$

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