
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
Consider a circle with equation \((x - a)^2 + (y - b)^2 = c^2\) and the function \( y = \cos x \). Determine the maximum number of points at which the circle can intersect the graph of \( y = \cos x \).
A) at most 2 points
B) at most 4 points
C) at most 6 points
D) at most 8 points
E) more than 16 points

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