
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 $\overrightarrow{a}$ and $\overrightarrow{b}$ with an angle of $60^{\circ}$ between them, and $|\overrightarrow{a}|=4$, $|\overrightarrow{b}|=2$,
(1) Find $\overrightarrow{a} \cdot \overrightarrow{b}$;
(2) Find $|\overrightarrow{a} + \overrightarrow{b}|$.

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