
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 non-zero vectors $m$ and $n$ with an angle of $\frac{\pi}{3}$ between them, and $|n| = λ|m| (λ > 0)$. The vector group $x_1$, $x_2$, $x_3$ is composed of one $m$ and two $n$'s, while the vector group $y_1$, $y_2$, $y_3$ is composed of two $m$'s and one $n$. If the minimum possible value of $x_1 \cdot y_1 + x_2 \cdot y_2 + x_3 \cdot y_3$ is $4m^2$, find the value of $λ$.

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