
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
Given condition \\(p\\): \\({{k}^{2}}+3k-4\leqslant 0\\); condition \\(q\\): the function \\(f\left( x \right)=\dfrac{1}{2}{{x}^{2}}+kx+\ln x\\) is increasing in its domain. If \\(p\wedge q\\) is false, and \\(p\vee q\\) is true, find the range of the real number \\(k\\).

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