
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 an integer $n \geq 4$, the set $M=\{1, 2, 3, \ldots, n\}$ has all subsets of 3 elements denoted as $A_{1}, A_{2}, \ldots, A_{C_{n}^{3}}$.  
(1) When $n=5$, find the sum of all elements in the sets $A_{1}, A_{2}, \ldots, A_{C_{5}^{3}}$.  
(2) Let $m_{i}$ be the smallest element in $A_{i}$, and let $P_{n} = m_{1} + m_{2} + \ldots + m_{C_{n}^{3}}$, try to find $P_{n}$.

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