
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 two lines $l_{1}:x\cos a+ \frac{1}{2}y-1=0$ and $l_{2}:y=x\sin a(a+ \frac{π}{6})$ in triangle $ABC$, where sides $a$, $b$, and $c$ correspond to angles $A$, $B$, and $C$ respectively, and when $a=B$, the two lines are perpendicular to each other.

(I) Find the value of $B$.
(II) If $\frac{c}{a}+ \frac{a}{c}=4$, 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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