
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
If $k$ is a real number within the interval $[-2, 2]$, find the probability of the value of $k$ that allows two lines passing through point $A(1, 1)$ to be tangent to the circle ${{x}^{2}}+{{y}^{2}}+kx-2y-\frac{5}{4}k=0$.

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