
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 $f(x)=3\sin ^{2}(x+ \frac {π}{6})+ \frac { \sqrt {3}}{2}\sin x\cos x- \frac {1}{2}\cos ^{2}x$.
(1) Find the maximum and minimum values of the function $f(x)$ on $[0, \frac {π}{2}]$.
(2) Given $f(2x_{0})= \frac {49}{20}$, where $x_{0}∈( \frac {π}{6}, \frac {7π}{24})$, find the value of $\cos 4x_{0}$.

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