
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
In the Cartesian coordinate system $xOy$, the equation of curve $C$ is $x^{2}+y^{2}=16$, and the parameter equation of the line is $\left\{\begin{array}{l}x=1+t\cos \theta \\y=2+t\sin \theta \end{array}\right.$ (where $t$ is the parameter). If the line $l$ intersects curve $C$ at points $M$ and $N$, and the midpoint of line segment $MN$ is $(1,2)$, calculate the slope of the line.

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