
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 $\{a_n\}$ with the sum of the first $n$ terms denoted as $S_n$, and it is known that $a_3=5$, $S_3=9$,

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

(2) Suppose the sum of the first $n$ terms of a geometric sequence $\{b_n\}$ is denoted as $T_n$, if $q > 0$, and $b_3=a_5$, $T_3=13$, find $T_n$.

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