
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
For the system of inequalities in terms of $x$
$$
\begin{cases}
x^{2}-x-2>0\\
2x^{2}+(2k+5)x+5k<0
\end{cases}
$$
the solution set is denoted as $A$. If set $A$ contains exactly one integer, find the range of the real number $k$.

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