
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 $f(x)=4\cos x\sin \left(x+ \frac {\pi}{6}\right)-1$,  
(I) find the interval of monotonic increase for $f(x)$  
(II) If $\sin ^{2}x+af\left(x+ \frac {\pi}{6}\right)+1 > 6\cos ^{4}x$ holds for any $x\in\left(- \frac {\pi}{4}, \frac {\pi}{4}\right)$, find the range of the real number $a$.

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