
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 unit vectors $e\_1$ and $e\_2$ with an angle of $\frac{π}{3}$ between them, and vectors $b\_1 = e\_1 - 2e\_2$ and $b\_2 = 3e\_1 + 4e\_2$, calculate the dot product $b\_1 · b\_2$.

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