
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 that $\overrightarrow {a}$=(1,2) and $\overrightarrow {b}$=(-3,1),
1. If $|\overrightarrow {c}|=2\sqrt {5}$ and $\overrightarrow {c}$ is parallel to $\overrightarrow {a}$, find $\overrightarrow {c}$;
2. If the vector $\overrightarrow {a}$+k$\overrightarrow {b}$ is perpendicular to $\overrightarrow {a}$-k$|\overrightarrow {b}|$, find the value of k.

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