
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
A direction vector of line $l$ is $\overrightarrow{\nu} = (4, -4)$, and its intersection with the $y$-axis is at point $(0, -4)$. Find the minimum value of $\overrightarrow{OM} \cdot \overrightarrow{ON}$ for two moving points $M$ and $N$ on line $l$ such that $|MN| = 4$.

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