
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
Suppose \( a, b, c \in \mathbf{R}^{+} \). Let \( M = \sqrt[4]{\frac{a}{b+c}} + \sqrt[4]{\frac{b}{c+a}} + \sqrt[4]{\frac{c}{b+a}} + \sqrt{\frac{b+c}{a}} + \sqrt{\frac{a+c}{b}} + \sqrt{\frac{a+b}{c}} \). Find the minimum value of \( M \).

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