
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 vectors $\overrightarrow{m}= (\sqrt {3}\sin x,\sin x)$, $\overrightarrow{n}=(\cos x,\sin x)$, and the function $f(x)= \overrightarrow{m}\cdot \overrightarrow{n}- \frac {1}{2}$ $(x\in\mathbb{R})$  
(I) Find the maximum value of the function $f(x)$ and its intervals of monotonic increase;  
(II) In $\triangle ABC$, the sides opposite angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively, satisfying $b^{2}=ac$ and $f(B)= \frac {1}{2}$. Find the value of $\left( \frac {1}{\tan A}+ \frac {1}{\tan C} \right)$.

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