
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
In a geometric sequence $\{a_n\}$ where all terms are positive, $a_1=1$, and $a_2+a_3=6$.  
(I) Find the general formula for the sequence $\{a_n\}$.  
(II) If $b_n= \begin{cases} 2n-1, & \text{n is odd} \\ a_n, & \text{n is even} \end{cases}$, 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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