
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 $\overrightarrow {m}=(\sin x，-1)$ and $\overrightarrow {n}=( \sqrt {3}\cos x，- \frac {1}{2})$, and the function $f(x)= \overrightarrow {m}^{2}+ \overrightarrow {m}\cdot \overrightarrow {n}-2$.
(I) Find the maximum value of $f(x)$ and the set of values of $x$ at which the maximum is attained.
(II) Given that $a$, $b$, and $c$ are the sides opposite to angles $A$, $B$, and $C$ of triangle $ABC$, respectively, and that they form a geometric sequence. Also, angle $B$ is acute, and $f(B)=1$. Find the value of $\frac{1}{\tan A} + \frac{1}{\tan C}$.

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