
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. In the Cartesian coordinate system, given three points A(5, 4), B(k, 10), and C(12, -2), for what value of k are the vectors $$\overrightarrow {AB}$$ and $$\overrightarrow {BC}$$ collinear?
2. In the Cartesian coordinate system, given O as the origin, $$\overrightarrow {OA}=(-7, 6)$$, $$\overrightarrow {OB}=(3, k)$$, $$\overrightarrow {OC}=(5, 7)$$, for what value of k are the vectors $$\overrightarrow {AB}$$ and $$\overrightarrow {BC}$$ perpendicular?

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