
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
Calculate the remainder when dividing $\frac{5}{9}$ by $-\frac{3}{7}$ using the remainder function defined as $\text{rem}(x, y) = x - y \left\lfloor \frac{x}{y} \right\rfloor$.
A) $\frac{-37}{63}$
B) $\frac{-19}{63}$
C) $\frac{-13}{63}$
D) $\frac{-25}{63}$
E) $\frac{19}{63}$

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