
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 binomial coefficient of the fifth term to the third term in the expansion of ${\left(\sqrt[3]{x}-\frac{1}{2\sqrt[3]{x}}\right)}^{n}$ is $14:3$.

(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}
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