
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
Let \(\alpha\) and \(\beta\) be the real roots of \(y^{2} - 6y + 5 = 0\). Let \(m\) be the minimum value of \(|x - \alpha| + |x - \beta|\) over all real values of \(x\). Find the value of \(m\).

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