
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 $\overrightarrow{e\_1}$ and $\overrightarrow{e\_2}$ are two unit vectors with an angle of $\frac{\pi}{3}$ between them, and $\overrightarrow{a} = 2\overrightarrow{e\_1} + \overrightarrow{e\_2}$, $\overrightarrow{b} = -3\overrightarrow{e\_1} + 2\overrightarrow{e\_2}$, find $\overrightarrow{a} \cdot \overrightarrow{b} = \_\_\_\_\_\_\_ \cdot$

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