
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 circle with center at \( (0,0) \) and radius \( 2 \) is plotted on the coordinate plane. Determine the number of intersections between this circle and the graph of \( y = \sin x \) if the \( x \)-values are restricted to \( [-2\pi, 2\pi] \).

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