
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
Simplify and evaluate the function: $$f(\theta)= \frac {(1+sin\theta+cos\theta)(sin \frac {\theta}{2}-cos \frac {\theta}{2})}{ \sqrt {2+2cos\theta}}$$, where $\theta \in [\pi, 2\pi]$ and $tan\theta=2$. Find $f(\theta)$.

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