
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
Let proposition \\(p\\): The equation \\( \dfrac{{x}^{2}}{2+k}- \dfrac{{y}^{2}}{3k+1}=1 \\) represents a hyperbola; proposition \\(q\\): A line with slope \\(k\\) passes through the fixed point \\(p(-2,1)\\), and has two distinct common points with the parabola \\({y}^{2}=4x\\. If \\(p∧q \\) is true, find the range of values for \\(k\\).

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