
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 $f(x)= \sqrt {3}\cos ( \frac {π}{2}+x)\cdot \cos x+\sin ^{2}x$, where $x\in R$.
(I) Find the interval where $f(x)$ is monotonically increasing.
(II) In $\triangle ABC$, angles $A$, $B$, and $C$ have corresponding opposite sides $a$, $b$, and $c$. If $B= \frac {π}{4}$, $a=2$, and angle $A$ satisfies $f(A)=0$, find the area of $\triangle ABC$.

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