
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
(I) Several cuboids with edge lengths of 2, 3, and 5 are assembled in the same direction to form a cube with an edge length of 90. The number of small cuboids that a diagonal of the cube passes through is  
A．64       B．66     C．68       D．70  
(II) Inside the circle $C: x^2+y^2-24x-28y-36=0$, there is a point $Q(4,2)$. A perpendicular chord $AQB$ intersects the circle at $A$ and $B$. Find the equation of the trajectory of the midpoint of the moving chord $AB$.

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