
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
Two points rotate uniformly around two concentric circles. One makes a complete revolution 5 seconds faster than the other, and thus manages to make two more revolutions per minute. At the start of the motion, the rays directed from the center of the circles to these points coincide. Calculate the magnitude of the angle between the rays after $1$ second.

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