
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
Define the "harmonic mean" of $n$ positive numbers $p_1, p_2, \ldots, p_n$ as $$\frac {n}{p_{1}+p_{2}+\ldots+p_{n}}$$. If it is known that the harmonic mean of the first $n$ terms of the sequence $\{a_n\}$ is $\frac {1}{2n+1}$,
(Ⅰ) Find the general term formula for the sequence $\{a_n\}$;
(Ⅱ) Let $d_n = 2^n \cdot a_n$, calculate the sum of the first $n$ terms, denoted as $T_n$, of the sequence $\{d_n\}$.

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