
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 the expansion of $( \frac{a}{x}- \sqrt{x})^{6}$ $(a > 0)$, the constant term is $60$.
(1) Find $a$;
(2) Find the coefficient of the term containing ${x}^{\frac{3}{2}}$;
(3) Find all the rational terms in the expansion.

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