
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
In the expansion of the binomial \((\sqrt{x} + \frac{1}{2\cdot\sqrt[6]{x}})^n\), the coefficients of the first three terms form an arithmetic sequence. Rearrange all the terms of the expansion such that no two rational terms are adjacent. Determine the probability of this arrangement.

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