
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 $ \frac {\pi}{2}\leqslant \beta\leqslant \alpha\leqslant \frac {3\pi}{4} $, $ \cos (\alpha-\beta) = \frac {12}{13} $, $ \sin (\alpha+\beta) = -\frac {3}{5} $, find the values of $ \sin 2\alpha $ and $ \cos 2\beta $.

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