
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) A unit has 160 employees, including 104 salespeople, 32 administrators, and 24 logistics personnel. If a sample of 20 people is to be drawn using stratified sampling, the number of administrators in the 20-person sample should be ______.

(2) Given the ellipse $\dfrac{x^2}{10-m} + \dfrac{y^2}{m-2} = 1$ with its major axis on the y-axis and a focal distance of 4, then $m=$ ______.

(3) Given the function $f(x) = -x^3 + ax - 4$ $(a \in R)$, if the tangent line to the graph of $y=f(x)$ at the point $P(1, f(1))$ has an inclination angle of $\dfrac{\pi}{4}$, then $a=$ ______.

(4) Let $F$ be the focus of the parabola $y^2 = 4x$, and let $A, B, C$ be three points on the parabola. If $\overrightarrow{FA} + \overrightarrow{FB} + \overrightarrow{FC} = \overrightarrow{0}$, then $|\overrightarrow{FA}| + |\overrightarrow{FB}| + |\overrightarrow{FC}| =$ ______.

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