
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
(1) The equation of the tangent line to the curve $y=x(3\ln x+1)$ at the point $(1,1)$ is __________.

(2) The sequence $\{a_n\}$ satisfies $a_1=1$, $a_{n+1}=\frac{a_n}{1+a_n}$ $(n\in \mathbb{N}^*)$, the general formula of the sequence is __________.

(3) If the curve $f(x)=\ln x+ax$ has a tangent line parallel to the line $2x-y=0$, then the range of the real number $a$ is __________.

(4) For natural numbers $m$ greater than $1$, the cube of $m$ can be "split" in the following way using odd numbers: $2^3=\begin{cases} 3, \\ 5, \end{cases}3^3=\begin{cases} 7, \\ 9, \\ 11, \end{cases}4^3=\begin{cases} 13, \\ 15, \\ 17, \\ 19, \end{cases}\ldots$. Accordingly, if one of the "split numbers" of $m^3$ is $2015$, then $m=$ __________.

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