
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 points $M$ and $N$ are two distinct points on the parabola $y = 4x^{2}$, and $F$ is the focus of the parabola, satisfying $\angle MFN = \frac{2\pi}{3}$. The distance from the midpoint $P$ of chord $MN$ to the line $l: y = -\frac{1}{16}$ is denoted as $d$. If $|MN|^{2} = \lambda d^{2}$, then calculate the minimum value of $\lambda$.

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