
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
Please use the formula $\left(a+b+c\right)^{2}=a^{2}+b^{2}+c^{2}+2ab+2ac+2bc$ to solve the following problem: Given $a$,$b$,$c$ satisfy $a^{2}+b^{2}+c^{2}=6$, then the minimum value of $\left(a+b\right)^{2}+\left(b+c\right)^{2}+\left(c+a\right)^{2}$ is ______.

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