
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 function $f(x)=x^{3}-x+3$ at $x=1$ is _______.

(2) The conjugate of the complex number $z=\frac{2+i}{1-i}$ (where $i$ is the imaginary unit) is _______.

(3) The maximum value of the function $y=\frac{\ln x}{x}$ is _______.

(4) Given a sequence of integer pairs as follows: $(1,1)$, $(1,2)$, $(2,1)$, $(1,3)$, $(2,2)$, $(3,1)$, $(1,4)$, $(2,3)$, $(3,2)$, $(4,1)$, $(1,5)$, $(2,4)$… The 57th pair in the sequence is _______.

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