
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
Let $\{a_n\}$ be an increasing geometric sequence, given that $a_1+a_3=5$, and $a_1+3$, $3a_2$, $a_3+4$ form an arithmetic sequence.  
(1) Find the general term of the sequence $\{a_n\}$.  
(2) Let $b_n=\ln a_{3n+1}$, for $n=1,2,\ldots$, 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}
user