
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]


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At the amusement park attraction "Fun Parking," the car has only 2 steering positions: "right" and "hard right." Depending on the steering position, the car travels along an arc with a radius of \(r_1\) or \(r_2\). The car left point \(A\) heading north and traveled a distance \(S\), turning through an angle \(\alpha < 2\pi\). Where could it end up? (Find the locus of the endpoints of possible trajectories).

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