
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 a finite set
$$
A = \left\{a_{i} \mid 1 \leq i \leq n, i \in \mathbf{Z}_{+}\right\} \left( n \in \mathbf{Z}_{+} \right), 
$$
let $S = \sum_{i=1}^{n} a_{i}$, so $S$ is called the "sum" of set $A$ and is denoted as $|A|$. The set $P = \{2n-1 \mid n=1,2,\cdots,10\}$ is given, and the set of all three-element subsets of $P$ is denoted as $P_{1}, P_{2}, \cdots, P_{k}$. Find $\sum_{i=1}^{k} \left|P_{i}\right|$.

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