
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 triangle $ABC$, the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$, respectively. It is known that $a$, $b$, and $c$ form a geometric sequence, and $\cos B= \frac {3}{4}$.

(I) Find the value of $\frac{1}{\tan A} + \frac{1}{\tan C}$;

(II) Given that $\overrightarrow{BA} \cdot \overrightarrow{BC} = \frac{3}{2}$, find the value of $a+c$.

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