
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) Given $f(\theta) = \frac{2\cos^{2}\theta + \sin^{3}(2\pi - \theta) + \cos(\frac{\pi}{2} + \theta) - 3}{2 + 2\sin(\pi + \theta) + \sin(-\theta)}$, find the value of $f(\frac{\pi}{6})$.

(2) Given $\tan \alpha = 2$, find the value of $\frac{2}{3}\sin^{2}\alpha + \sin\alpha\cos\alpha + \frac{1}{4}\cos^{2}\alpha - 2$.

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