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

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