
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 vectors $\overrightarrow {a}$, $\overrightarrow {b}$, $\overrightarrow {c}$ are in the same plane, and $\overrightarrow {a}=(-1,2)$.  
(1) If $\overrightarrow {c}=(m-1,3m)$ and $\overrightarrow {c} \parallel \overrightarrow {a}$, find the value of $m$;  
(2) If $|\overrightarrow {a}- \overrightarrow {b}|=3$ and $(\overrightarrow {a}+2 \overrightarrow {b}) \perp (2 \overrightarrow {a}- \overrightarrow {b})$, find the angle between the vector $\overrightarrow {a}- \overrightarrow {b}$ and $\overrightarrow {b}$.

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