
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 \(a, b, c\) are positive real numbers, and \(a + b + c = 1\), find the minimum value of \(u = \frac{3a^{2} - a}{1 + a^{2}} + \frac{3b^{2} - b}{1 + b^{2}} + \frac{3c^{2} - c}{1 + c^{2}}\).

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