
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:
\[
\begin{cases}
x^2 - x - 2 > 0 \\
2x^2 + (5 + 2k)x + 5 < 0
\end{cases}
\]
with the integer solution set \(\{-2\}\), find the range of \(k\).

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