
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 \(a > 0\), \(b > 0\), \(c > 1\), and \(a + b = 1\). Find the minimum value of \(\left(\frac{2a + b}{ab} - 3\right)c + \frac{\sqrt{2}}{c - 1}\).

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