
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
Suppose $\overrightarrow{e_{1}}$ and $\overrightarrow{e_{2}}$ are two unit vectors with an angle of $60^{\circ}$ between them, and $\overrightarrow{a} = 2\overrightarrow{e_{1}} + \overrightarrow{e_{2}}$, $\overrightarrow{b} = -3\overrightarrow{e_{1}} + 2\overrightarrow{e_{2}}$.  
(1) Calculate $\overrightarrow{a} \cdot \overrightarrow{b}$.  
(2) Calculate $|\overrightarrow{a}|$ and $|\overrightarrow{b}|$.  
(3) Calculate the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$.

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