
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
Let $a = \log(z) + \log\left(\frac{x}{yz} + 1\right)$, $b = \log\left(\frac{1}{x}\right) + \log(xyz + 1)$, $c = \log(y) + \log\left(\frac{1}{xyz} + 1\right)$. Denote the largest number among $a$, $b$, and $c$ as $M$. The minimum value of $M$ is ______.

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