
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 $\overrightarrow{e_1}$ and $\overrightarrow{e_2}$ with an angle of $\frac{\pi}{3}$ between them, if vector $\overrightarrow{b_1} = 2\overrightarrow{e_1} - 4\overrightarrow{e_2}$ and $\overrightarrow{b_2} = 3\overrightarrow{e_1} + 4\overrightarrow{e_2}$, then find the dot product $\overrightarrow{b_1} \cdot \overrightarrow{b_2}$.

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