
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 a geometric sequence $\{a_n\}$, the sum of its first $n$ terms is $S_n$. It is known that $a_1+a_4=-\frac{7}{16}$, and for any $n\in\mathbb{N}^*$, $S_n$, $S_{n+2}$, $S_{n+1}$ form an arithmetic sequence;  
(Ⅰ) Find the general formula for the sequence $\{a_n\}$;  
(Ⅱ) Given $b_n=n$ ($n\in\mathbb{N}_+$), let $T_n=|\frac{b_1}{a_1}|+|\frac{b_2}{a_2}|+|\frac{b_3}{a_3}|+\ldots+|\frac{b_n}{a_n}|$. If $(n-1)^2\leqslant m(T_n-n-1)$ holds for $n\geqslant 2$, find the range of the real number $m$.

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