
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) In the Cartesian coordinate system $xOy$, the focal length of the hyperbola $\dfrac{x^2}{7} - \dfrac{y^2}{3} = 1$ is ______.

(2) The solution set of the inequality $\dfrac{x-2}{x-1} < 0$ is ______.

(3) Given $F_1(-4,0)$, $F_2(4,0)$, a moving point $M$ satisfies $|MF_1| + |MF_2| = 10$, then the trajectory equation of the moving point $M$ is ______.

(4) Given the hyperbola $\dfrac{x^2}{16} - \dfrac{y^2}{9} = 1$, a point $P$ on the left branch of the hyperbola is at a distance of $10$ from the left focus, then the distance from point $P$ to the right focus is ______.

(5) If the sequence $\{a_n\}$ satisfies $a_1=2$, $a_1+a_2+a_3+\ldots+a_n=na_n$, then $a_{2017}=$ ______.

(6) Given that the point $(1,1)$ is the midpoint of a chord of the hyperbola $\dfrac{x^2}{4} - \dfrac{y^2}{2} = 1$, then the equation of the line containing this chord is ______.

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