
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 three vectors $\overset{→}{a}$, $\overset{→}{b}$, and $\overset{→}{c}$ in the same plane, where $\overset{→}{a} = (1, -1)$.

(I) If $|\overset{→}{c}| = 3\sqrt{2}$ and $\overset{→}{c}$ is parallel to $\overset{→}{a}$, find the coordinates of vector $\overset{→}{c}$.

(II) If $|\overset{→}{b}| = 1$ and $\overset{→}{a}$ is perpendicular to $(\overset{→}{a} - 2\overset{→}{b})$, find the angle $q$ between $\overset{→}{a}$ and $\overset{→}{b}$.

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