
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 in the expansion of the binomial $\left(\sqrt [3] {x}+\dfrac{1}{2\sqrt [3] {x}}\right)^{n}$, the absolute values of the coefficients of the first three terms form an arithmetic sequence.

1. Find the value of the positive integer $n$.
2. Find the term with the largest coefficient in the expansion.
3. Find the term with the largest coefficient in the expansion.

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