
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 directrix of the parabola $y=ax^{2}$ is $y=1$. The value of $a$ is ______.

(2) Let $l$ be the tangent line to the curve $C: y=\frac{\ln x}{x}$ at the point $(1,0)$. The equation of $l$ is ______.

(3) Given the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{25}=1$, with foci $F_{1}$ and $F_{2}$, and chord $AB$ passing through $F_{1}$, the perimeter of $\triangle ABF_{2}$ is ______.

(4) Given the function $f(x)=x^{2}-m\ln x$ is monotonically increasing on $[2,+\infty)$, the range of the real number $m$ is ______.

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