
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 an arithmetic sequence $\{a_n\}$ have a first term of 1, and let $a_2$, $a_5$, and $a_{14}$ form a geometric sequence with the common difference not equal to 0.  
(I) Find the general formula for the sequence $\{a_n\}$.  
(II) If the sequence $\{b_n\}$ satisfies $$\frac {b_{1}}{a_{1}}+ \frac {b_{2}}{a_{2}}+…+ \frac {b_{n}}{a_{n}}=1- \frac {1}{2^{n}}$$, where $n\in\mathbb{N}^{*}$, find the sum of the first $n$ terms of $\{b_n\}$, denoted as $T_n$.

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