
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
(1) Find the fourth term in the expansion of $\left( x+ \frac{2}{x} \right)^{6}$;

(2) Given that the ratio of the binomial coefficients of the fifth term to the third term in the expansion of $\left( \sqrt{x}- \frac{2}{x^{2}} \right)^{n}$ is $14:3$, find the constant term in the expansion.

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