
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 sequence $\{a_n\}$ where the sum of its first $n$ terms $S_n$ satisfies $S_{n+1}=2S_n+1$, and $a_1=1$.

(I) Find the general formula for the $n$-th term $a_n$ of the sequence $\{a_n\}$.
(II) Find the sum of the first $n$ terms $T_n$ of the sequence $\{na_n\}$.

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