
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 the sequence $\{a\_n\}$ that satisfies $a\_n=3a_{n-1}+3^{n}(n\\geqslant 2,n\\in\\mathbb{N}^{\\ast})$, with the first term $a\_1=3$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Find the sum of the first $n$ terms, denoted as $S\_n$.
3. The sequence $\{b\_n\}$ satisfies $b\_n=\\log \_{3} \\frac {a\_n}{n}$. Let $T\_n$ denote the sum of the first $n$ terms of the sequence $\{ \\frac {1}{b\_n\\cdot b_{n+1}}\\}$. $A$ is an internal angle of $\\triangle ABC$. If $\\sin A\\cos A > \\frac { \\sqrt {3}}{4}T\_n$ holds true for any $n\\in\\mathbb{N}^{\\ast}$, find the range of angle $A$.

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