
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 the system of inequalities with respect to \( x \):
\[
\begin{cases} 
x^{2}-x-2>0 \\ 
2 x^{2}+(2k+5)x+5k<0 
\end{cases}
\]
The set of integer solutions is \( \{-2\} \). Find the range of values for the real number \( k \).

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