
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 in the expansion of $(3x - \frac{1}{2 \cdot 3x})^n$ ($n \in \mathbb{N}^*$), the sixth term is a constant term.  
(1) Find the value of $n$ and the coefficient of the term containing $x^2$;  
(2) ① Find all rational terms in the expansion;  
② Find the term in the expansion with the largest absolute value of the coefficient.

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