
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 $xOy$, with the origin $O$ as the pole and the $Ox$ axis as the polar axis, a polar coordinate system is established. The equation of curve $C_{1}$ is $\begin{cases} & x=\dfrac{1}{\tan \phi} \\ & y=\dfrac{1}{{\tan}^{2}\phi} \end{cases}(\phi$ is the parameter), and the polar equation of curve $C_{2}$ is: $\rho (\cos \theta +\sin \theta )=1$. If curve $C_{1}$ intersects with $C_{2}$ at points $A$ and $B$.

$(I)$ Find the value of $|AB|$;           

$(II)$ Find the product of the distances from point $M(-1,2)$ to points $A$ and $B$.

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