
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 real numbers \(a \), \(b\), and \(c\) such that \(a^{2}+b^{2}+c^{2}=\lambda(\lambda>0)\), find the maximum value of \( f = \min \left\{(a-b)^{2},(b-c)^{2},(c-a)^{2}\right\} \).

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