
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
An arithmetic sequence \(\{a_n\}\) with distinct terms has a sum of the first four terms \(S_4 = 14\) and the terms \(a_1\), \(a_3\), \(a_7\) form a geometric sequence.
(1) Find the general term formula for the sequence \(\{a_n\}\).
(2) Let \(T_n\) be the sum of the first \(n\) terms of the sequence \(\left\{ \frac {a_{n-1}}{2^n}\right\}\), find \(T_n\).

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