
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 $f(x)=2 \sqrt {3}\sin \frac {ωx}{2}\cos \frac {ωx}{2}-2\sin ^{2} \frac {ωx}{2}(ω > 0)$ with a minimum positive period of $3π$.
(I) Find the interval where the function $f(x)$ is monotonically increasing.
(II) In $\triangle ABC$, $a$, $b$, and $c$ correspond to angles $A$, $B$, and $C$ respectively, with $a < b < c$, $\sqrt {3}a=2c\sin A$, and $f(\frac {3}{2}A+ \frac {π}{2})= \frac {11}{13}$. Find the value of $\cos B$.

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