
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 $S_{n}$ is the sum of the first $n$ terms of an arithmetic sequence $\{a_{n}\}$, with $a_{2}=1$. Choose one of the following conditions: ① $2a_{5}-a_{3}=11$; ② $S_{4}=8$. Solve the following problems:  
$(1)$ Find the general term of the sequence $\{a_{n}\}$;  
$(2)$ Let $b_{n}=\frac{1}{{S}_{n+2}}$, compare the sum of the first $n$ terms of the sequence $\{a_{n}\}$ denoted by $T_{n}$ with $\frac{3}{4}$.

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