
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
If the system of inequalities with respect to $x$: 
\[
\left\{
\begin{array}{l}
x^{3} + 3x^{2} - x - 3 > 0 \\
x^{2} - 2ax - 1 \leqslant 0
\end{array}
\right., \quad (a > 0)
\]
has exactly one integer solution, then determine the range of values for $a$.

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