
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
Evaluate $\text{rem}\left(-\tfrac{1}{7}, \tfrac{1}{3} \right)$ using the remainder definition $\text{rem}(x, y) = x - y \left\lfloor \frac{x}{y} \right\rfloor$, where $\left\lfloor \tfrac{x}{y} \right\rfloor$ is the greatest integer less than or equal to $\tfrac{x}{y}$.

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