
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
Larry and Rob are two robots traveling in one car from Argovia to Zillis. Both robots have control over the steering and follow these rules: Larry makes a $90^{\circ}$ left turn after every $\ell$ kilometers starting from the beginning; Rob makes a $90^{\circ}$ right turn after every $r$ kilometers starting from the beginning, where $\ell$ and $r$ are relatively prime positive integers. If both turns happen simultaneously, the car continues straight. Assume the ground is flat and the car can move in any direction.

For which pairs $(\ell, r)$ is the car guaranteed to reach Zillis, regardless of the distance from Argovia?

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