
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 $x$: $\left\{{\begin{array}{l}{\frac{{x+2}}{{4-x}}＜0}\\{2{x^2}+({2a+7})x+7a＜0({a∈R})}\end{array}}\right.$ has only one integer solution, then the range of values for $a$ is ______.

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