
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 $\overrightarrow {a}$ and $\overrightarrow {b}$ are two unit vectors.
(1) If $|3 \overrightarrow {a}-2 \overrightarrow {b}|=3$, find the value of $|3 \overrightarrow {a}+ \overrightarrow {b}|$.
(2) If the angle between $\overrightarrow {a}$ and $\overrightarrow {b}$ is $\frac {π}{3}$, find the angle α between the vectors $\overrightarrow {m}=2 \overrightarrow {a}+ \overrightarrow {b}$ and $\overrightarrow {n}=2 \overrightarrow {b}-3 \overrightarrow {a}$.

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