
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 the function $f(x) = \ln x$ with its domain as $(M, +\infty)$, and $M > 0$. Also, for any $a, b, c \in (M, +\infty)$, if $a, b, c$ are the lengths of the sides of a right-angled triangle, and $f(a), f(b), f(c)$ can also form the sides of a triangle, find the minimum value of $M$.

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