
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 $\overrightarrow{a} = (2, 0)$ and $\overrightarrow{b} = (1, 4)$,
(1) Find $2\overrightarrow{a} + 3\overrightarrow{b}$ and $\overrightarrow{a} - 2\overrightarrow{b}$.
(2) If vector $k\overrightarrow{a} + \overrightarrow{b}$ is parallel to $\overrightarrow{a} + 2\overrightarrow{b}$, find the value of $k$.

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