
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 that the angle between vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ is 120°, and the magnitude of $\overrightarrow {a}$ is 2, and the magnitude of $\overrightarrow {b}$ is 3, let $\overrightarrow {m}$ = $3 \overrightarrow {a}$ - $2 \overrightarrow {b}$, and $\overrightarrow {n}$ = $2 \overrightarrow {a}$ + $k \overrightarrow {b}$
1. If $\overrightarrow {m}$ is perpendicular to $\overrightarrow {n}$, find the value of the real number $k$;
2. When $k$ = $\frac {8}{3}$, find the angle $\theta$ between vectors $\overrightarrow {m}$ and $\overrightarrow {n}$.

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