
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 two vectors in the plane $\overrightarrow{a}=(3,1)$ and $\overrightarrow{b}=(-1,2)$:
1. Calculate the magnitude of $3\overrightarrow{a} + 2\overrightarrow{b}$.
2. If $(\overrightarrow{a} + k\overrightarrow{b}) \parallel (2\overrightarrow{a} - \overrightarrow{b})$, find the value of the real number $k$.

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