
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
The function is given by $$f(x)=( \frac {a}{x}+ \sqrt {x})^{9}$$ where $a$ is a real number constant.
(1) The coefficient of the $x^3$ term in the expansion of $f(x)$ is known to be $\frac {9}{4}$. Find the value of $a$.
(2) Given that $a>0$, find the range of $a$ such that $f(x) \geq 27$ holds true for any value of $x$ within the domain.

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