
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 sequence $\{a\_n\}$ that satisfies $\log\_3 a\_n + 1 = \log\_3 a\_{n+1}$ for all $n \in \mathbb{N}^*$, and $a\_2 + a\_4 + a\_6 = 9$, determine the value of $\log\_3 (a\_5 + a\_7 + a\_9)$.

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