
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 the line $l: (3m+1)x + (2+2m)y - 8 = 0$ (where $m$ is any real number) passes through a fixed point $P$, then the coordinates of point $P$ are ______; if the line $l$ intersects the lines $l_{1}: x=-1$ and $l_{2}: y=-1$ at points $M$ and $N$ respectively, then the minimum value of $|PM| \cdot |PN|$ is ______.

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