
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 not less than 3, and let $P = \{x | x \leqslant n, x \in \mathbb{N}^*\}$. Denote the sum of all elements in all $k$-element subsets of set $P$ as $P_k$, where $1 \leqslant k \leqslant n, k \in \mathbb{N}^*$.
(1) Find $P_1$ and $P_2$;
(2) Find $P_1 + P_2 + \dots + P_n$.

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