
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 an arithmetic sequence \(\{a_n\}\) where \(a_2=8\) and the sum of the first 10 terms \(S_{10}=185\).

(1) Find the general formula for the sequence \(\{a_n\}\).

(2) If a new sequence \(\{b_n\}\) is formed by taking the 2nd, 4th, 8th, ..., \(2^n\)th, ..., terms of the sequence \(\{a_n\}\) in the original order, find the sum of the first \(n\) terms of the sequence \(\{b_n\}\), denoted as \(T_n\).

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