
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 expansion of $(( 3x - \frac {1}{2 3x })^{n})$, the 6th term is a constant term.
(1) Find $n$;
(2) Find the coefficient of the term containing $x^{2}$;
(3) Find all the rational terms in the expansion.

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