
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
A particle moves in the $Oxy$ plane of a rectangular coordinate system according to the law (where $x, y$ are the coordinates of the point in meters, and $t$ is the time in seconds):

$$
x(t)=3+\sin t \cdot \cos t-\sin t-\cos t ; \quad y(t)=1
$$

In the same plane, a light ray constantly originates from the origin according to the law $y=c x$, where $c$ is a positive dimensionless constant. For which values of $c$ is there at least one moment in time when the given particle is illuminated by the light ray?

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