
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
(1) Calculate: $\cos \frac {9\pi}{4} + \tan(-\frac {\pi}{4}) + \sin 21\pi$;
(2) Given $\sin \theta = 2\cos \theta$, evaluate $\frac {\sin^2 \theta + 2\sin \theta \cos \theta}{2\sin^2 \theta - \cos^2 \theta}$.

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