
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
The sequence ${a_n}$ is a geometric sequence with a common ratio greater than $1$. $S_n$ is the sum of the first $n$ terms of ${a_n}$. Given that $S_3=7$, and $a_1+3$, $3a_2$, $a_3+4$ form an arithmetic sequence.

1. Find the general term formula for ${a_n}$.
2. Let $b_n=\frac{1}{(\log_2a_n+1)(\log_2a_{n+1}+1)}$. 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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