
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 $\text{rem}(x, y)$ for $x = \frac{5}{9}$ and $y = -\frac{3}{4}$ using the definition $\text{rem}(x, y) = x - y\left \lfloor \frac{x}{y} \right \rfloor$.

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