
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 $\{a_n\}$, where $a_1 = 1$ and $a_n > 0$, the sum of the first $n$ terms is denoted as $S_n$. The sequence $\{\sqrt{S_n}\}$ also forms an arithmetic sequence. Let $b_n= \dfrac{a_{n+2}}{2^n \cdot a_n \cdot a_{n+1}}$, then the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $T_n$, is equal to __________.

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