
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 $$\overrightarrow {a} = (1, 1)$$, $$\overrightarrow {b} = (3, 4)$$,  
(1) If $k \overrightarrow {a} + \overrightarrow {b}$ is perpendicular to $k \overrightarrow {a} - \overrightarrow {b}$, find the value of $k$;  
(2) If $|k \overrightarrow {a} + 2 \overrightarrow {b}| = 10$, find the value of $k$.

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