
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
(1) If $\overrightarrow{a} = (-3, 4)$ and $\overrightarrow{b} = (2, -1)$, and $(\overrightarrow{a} - x\overrightarrow{b})$ is perpendicular to $(\overrightarrow{a} - \overrightarrow{b})$, find the value of $x$;  
(2) Vectors $\overrightarrow{OA} = (k, 12)$, $\overrightarrow{OB} = (4, 5)$, $\overrightarrow{OC} = (10, k)$. For what value(s) of $k$ are points A, B, C collinear?

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