
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 $\overrightarrow{a}$ and $\overrightarrow{b}$ with an angle of $\frac{2\pi}{3}$ between them, $|\overrightarrow{a}|=2$, $|\overrightarrow{b}|=3$. Let $\overrightarrow{m} = 3\overrightarrow{a} - 2\overrightarrow{b}$ and $\overrightarrow{n} = 2\overrightarrow{a} + k\overrightarrow{b}$:
(I) If $\overrightarrow{m} \perp \overrightarrow{n}$, find the value of the real number $k$;
(II) When $k=-\frac{4}{3}$, determine the angle $\theta$ between vectors $\overrightarrow{m}$ and $\overrightarrow{n}$.

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