
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]


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Given a geometric series with positive terms $\{a_n\}$, the sum of the first $n$ terms is denoted as $S_n$, and it is given that $a_2a_3=a_5$ and $S_4=10S_2$.
(1) Find the general formula for the term $a_n$ of the series $\{a_n\}$.
(2) Define $b_n=(2n-1)a_n$. Calculate the sum of the first $n$ terms of the series $\{b_n\}$, denoted as $T_n$.

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