
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 function $y=a+8\ln x$ ($x\in[\frac{1}{e},e]$), there exists a point $P$ on its graph. There also exists a point $Q$ on the graph of the function $y=-x^2-2$. Points $P$ and $Q$ are symmetric about the $x$-axis. Determine the range of values for $a$.

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