
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 positive integer. Starting with the sequence 1, 2, 3, ..., $n$, we calculate the sum of each pair of adjacent terms to form a new sequence with $n-1$ terms: 1+2, 2+3, 3+4, ..., $(n-1)+n$, which is 3, 5, 7, ..., $2n-1$. Continue this operation on the new sequence to generate a series of sequences until the last sequence contains only one term.
(1) Denote the original sequence as the first sequence, then the $j$-th ($j \in \mathbb{N}^*$ and $1 \leq j \leq n-2$) term of the third sequence is $\boxed{4j+4}$;
(2) The term in the last sequence is $\boxed{(n+1) \cdot 2^{n-2}}$.

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