
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 $\overset{⇀}{a}$, $\overset{⇀}{b}$, and $\overset{⇀}{c}$ in the same plane, and $\overset{⇀}{a} = (-1, 2)$.
(1) If $\overset{⇀}{c} = (m - 1, 3m)$ and $\overset{⇀}{c}$ is parallel to $\overset{⇀}{a}$, find the value of $m$.
(2) If $|\overset{⇀}{a} - \overset{⇀}{b}| = 3$ and $(\overset{⇀}{a} + 2\overset{⇀}{b}) ⊥ (2\overset{⇀}{a} - \overset{⇀}{b})$, find the angle between the vectors $\overset{⇀}{a} - \overset{⇀}{b}$ and $\overset{⇀}{b}$.

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