
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 $n$ be a given positive integer no less than 3, and let the set $P=\{x|x\leq n, x\in \mathbb{N}^*\}$. Denote the sum of all elements of all $k$-element subsets of $P$ (where $1\leq k\leq n, k\in \mathbb{N}^*$) as $P_k$.  
(1) Find $P_1$ and $P_2$;  
(2) Find $P_1+P_2+\ldots+P_n$.

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