
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 vectors $$\overrightarrow {a}=(0,1,-1)$$ and $$\overrightarrow {b}=(1,0,2)$$, if vector $$k\overrightarrow {a}+\overrightarrow {b}$$ is perpendicular to vector $$\overrightarrow {a}-\overrightarrow {b}$$, find the value of k.

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