
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 the function $f(x)=3\sin \omega x\cos \omega x-4\cos ^{2}\omega x$, given that its period is $\pi$ and $f(\theta)= \frac {1}{2}$, determine the value of $f(\theta+ \frac {\pi}{2})+f(\theta- \frac {\pi}{4})$.

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