
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 \( f(x) = \frac{1}{a} x^{2} - 4x + 1, \, x \in [0,1] \), where the maximum value of the function is \( M(a) \) and the minimum value is \( m(a) \), find the expression for \( M(a) - m(a) \).

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