
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
Compute the remainder for $\text{rem}\left(-\frac{1}{3}, \frac{4}{7}\right)$ using the remainder function definition: $\text{rem}(x, y) = x - y \left \lfloor \frac{x}{y} \right \rfloor$ where $\left \lfloor \frac{x}{y} \right \rfloor$ is the greatest integer less than or equal to $\frac{x}{y}$ for non-zero $y$.

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