
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
If $\vec{e}_1$ and $\vec{e}_2$ are unit vectors with an angle of $\frac{\pi}{3}$ between them, and $\vec{a}=2\vec{e}_1+ \vec{e}_2$, $\vec{b}=-3\vec{e}_1+2\vec{e}_2$, calculate the value of $\vec{a}\cdot \vec{b}$.

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