
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 $f(x)=2\cos x\sin (x+ \frac {π}{6})+1$, $x\in R$.
(1) Find the smallest positive period of the function and the monotonically increasing interval in $[0,π]$;
(2) If $x\in[- \frac {π}{6}, \frac {π}{3}]$, find the range of the function.

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