
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 that \(a\), \(b\), and \(c\) are all positive numbers, determine the maximum value of 
\[ 
M = \min \left\{\frac{1}{a}, \frac{2}{b}, \frac{4}{c}, \sqrt[3]{abc}\right\}.
\]

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