
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 that the ratio of the coefficient of the 5th term to the coefficient of the 3rd term in the expansion of $(( \sqrt {x}- \frac {2}{ 3x })^{n})$ is $56:3$.
$(1)$ Find all the rational terms in the expansion;
$(2)$ Find the term with the largest absolute value of the coefficient in the expansion.
$(3)$ Calculate the value of $n+9c \;\_{ n }^{ 2 }+81c \;\_{ n }^{ 3 }+…+9^{n-1}c \;\_{ n }^{ n }$.

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