
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 $f(x)=- \sqrt {3}\sin x\sin (x+ \frac {π}{2})+{\cos ^{2}x- \frac {1}{2}}(x∈R)$.
(1) Find the interval(s) where the function $f(x)$ is monotonically increasing;
(2) If the horizontal coordinates of all points on the graph of $f(x)$ are doubled and then shifted to the right by $\frac {π}{6}$ units, obtain the graph of $g(x)$. Find the maximum and minimum values of the function $y=g(x)$ on the interval $[0,π]$.

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