
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) Given that the complex number $z$ satisfies $\frac{3+4i}{z}=5i$, find the value of $|z|$.

(2) Find the equation of the circle that is tangent to the asymptotes of the hyperbola $C:\frac{x^{2}}{4}-\frac{y^{2}}{5}=1$ and has the right focus of the hyperbola as its center.

(3) Given that the function $f(x)$ $(x\in R)$ satisfies $f(2)=1$ and its derivative $f'(x) > \frac{2}{3}$, find the solution set of the inequality $f(x) > \frac{2x}{3}-\frac{1}{3}$.

(4) Given the sequence of points in 3D space: $(1,1,1)$, $(1,1,2)$, $(1,2,1)$, $(2,1,1)$, $(1,1,3)$, $(1,3,1)$, $(3,1,1)$, $(1,2,2)$, $(2,1,2)$, $(2,2,1)$, $(1,1,4)$, $(1,4,1)$, $(4,1,1)$, $(1,2,3)$, $(1,3,2)$, $...$, find the position of $(4,2,1)$ in this sequence.

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