
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
Find the minimum value of \( M \) such that the function
$$
f(x) = x^2 - 2x + 1
$$

for any partition of the interval \([0, 4]\)
$$
0 = x_0 < x_1 < \cdots < x_{n-1} < x_n = 4,
$$

always satisfies
$$
\sum_{i=1}^{n} \left| f\left( x_i \right) - f\left( x_{i-1} \right) \right| \leqslant M.
$$

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