
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 three vectors in the plane, $\overrightarrow {a}=(3,2)$, $\overrightarrow {b}=(0,2)$, $\overrightarrow {c}=(4,1)$  
(1) Find the magnitude of $\overrightarrow{a}+\overrightarrow{b}$.  
(2) If $\overrightarrow{a}+k\overrightarrow{c}$ is parallel to $2\overrightarrow{a}-\overrightarrow{b}$, find the value of the real number $k$.

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