
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 functions $f\_1(x)=\sin ( \frac {3π}{2}+x)\cos x$ and $f\_2(x)=\sin x\sin (π+x)$, if we define $f(x)=f\_1(x)-f\_2(x)$, determine the interval(s) where $f(x)$ is monotonically increasing.

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