
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 $$\overrightarrow {a}=(1,2), \overrightarrow {b}=(-3,2)$$,  
① If $$k \overrightarrow {a}+ \overrightarrow {b}$$ is perpendicular to $$\overrightarrow {a}-3 \overrightarrow {b}$$, find the value of $k$;  
② If $$k \overrightarrow {a}+ \overrightarrow {b}$$ is parallel to $$\overrightarrow {a}-3 \overrightarrow {b}$$, find the value of $k$.

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