
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 $g(x) = a - x^3$ ($\frac{1}{e} \leq x \leq e$, where $e$ is the base of the natural logarithm) and the function $h(x) = 3\ln(x)$, there exist points on the graphs of $g$ and $h$ that are symmetrical about the x-axis. Find the range of the real number $a$.

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