
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
The function f(x) is defined as $$f(x) = \begin{cases} e^{\frac{a}{3}x}, & x \leq 0 \\ \frac{3\ln x}{x}, & x > 0 \end{cases}$$. The maximum value of f(x) on the interval [-3, 3] is $\frac{3}{e}$. Determine the range of values for the parameter a.

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