
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 $f(x)$ satisfies $f(x+3)=3f(x)$, when $x \in (0,3)$, $f(x)=\ln x-ax(a > \frac {1}{3})$, and when $x \in (-6,-3)$, the maximum value of $f(x)$ is $- \frac {1}{9}$. Find the value of the real number $a$.

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