
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 a sequence $\{a_n\}$ that satisfies $\log_{3}a_n+1=\log_{3}a_{n+1}$ $(n\in\mathbb{N}^*)$ and $a+a_4+a_6=9$, find the value of $\log_{\frac{1}{3}}(a_5+a_7+a_9)$.

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