
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
(1) Find the interval of increase for the function $$f(x)=2\cos x\sin\left(x+ \frac {\pi}{6}\right)$$;  
(2) Find the minimum value of the function $$y=3\cos^{2}x-4\cos x+1$$, where $$x\in[0, \frac {\pi}{2}]$$.

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