
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 $f(x) = x^2 - 2x$, where $a-1 \leq x \leq a+1$, $a \in \mathbb{R}$. Let the set $M = \{(m, f(n)) | m, n \in [a-1, a+1]\}$, if the area of the plane region enclosed by all points in $M$ is $S$, then the minimum value of $S$ is.

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