
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 $\{a_n\}$ satisfying: $a_4=6$, $a_6=10$.

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

(2) Suppose that a geometric sequence $\{b_n\}$ has all positive terms, and $T_n$ is the sum of its first $n$ terms. If $b_1=1$ and $b_3=a_3$, find $T_n$.

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