
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
Given the remainder function for real numbers $x$ and $y$ (with $y \neq 0$) as $\text{rem}(x,y)=x-y\left\lfloor \frac{x}{y} \right\rfloor$, calculate the value of $\text{rem}(\tfrac{5}{7} + \tfrac{1}{3}, -\tfrac{3}{4})$.
A) $-\frac{19}{42}$
B) $\frac{19}{42}$
C) $\frac{16}{63}$
D) $-\frac{16}{63}$

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