
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 function $f(x) = x^2 - 4x$, $x \in [a-1, a+1]$, $a \in \mathbb{R}$. Let $M = \{(m, f(n)) | m, n \in [a-1, a+1]\}$. If the area enclosed by all the points in $M$ is denoted as $S$, then the minimum value of $S$ is ______.

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