
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 $f(x)=3\sin ( \frac{x}{2} + \frac{π}{6} )+3$, $x\in R$.
(1) Find the minimum positive period and the interval where the function is monotonically increasing.
(2) If $x\in\[ \frac{π}{3}, \frac{4π}{3}\]$, find the maximum and minimum values of $f(x)$, and specify the corresponding $x$ values when $f(x)$ reaches these values.

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