
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
Arrange $\frac{n(n+1)}{2}$ different real numbers into a triangular number table, with $k$ numbers in the $k$th row ($k=1,2,\cdots,n$). Let the maximum number in the $k$th row be $M_{k}$. Find the probability that $M_{1}<M_{2}<\cdots<M_{n}$.

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