
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 sets
$$
\begin{array}{l}
A=\left\{x \mid x^{2}+2 x-8>0\right\}, \\
B=\left\{x \mid x^{2}-2 a x+4 \leq 0\right\}.
\end{array}
$$

If \( a > 0 \) and the intersection \( A \cap B \) contains exactly one integer, then find the range of values for \( a \).

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