
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
Given: \\(\sin^2 1^\circ + \sin^2 61^\circ + \sin^2 121^\circ = \frac{3}{2}\\) and \\(\sin^2 5^\circ + \sin^2 65^\circ + \sin^2 125^\circ = \frac{3}{2}\\)

Based on the pattern observed in the two equations above, please write a general proposition: _______________________________________________________________________

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