
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 that $|\overrightarrow{a}|=2$, $|\overrightarrow{b}|=3$, and the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is $60^{\circ}$.
(1) Find $\overrightarrow{a} \cdot \overrightarrow{b}$.
(2) Find $|\overrightarrow{a} + \overrightarrow{b}|$.
(3) Find the cosine value of the angle between $\overrightarrow{a} + \overrightarrow{b}$ and $\overrightarrow{a} - \overrightarrow{b}$.

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