
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 $f(x) = x^2 - 4x + 1$, and suppose that $1 \leq x_1 < x_2 < x_3 < \ldots < x_n \leq 4$, find the minimum value of $M$ such that $|f(x_1) - f(x_2)| + |f(x_2) - f(x_3)| + \ldots + |f(x_{n-1}) - f(x_n)| \leq M$.

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