
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
A certain type of tree seedling has a height of $A$ meters when it is planted. Let $f(x)$ denote the height of the tree $x$ years after planting. Through research, it is found that $f(x)$ can be approximated by the formula $f(x) = \frac{9A}{a + bt^2}$, where $t = 2^{-\frac{2}{3}}$, and $a$ and $b$ are constants. Given that the height of the tree is three times its initial height after 3 years, find:

(I) The analytical expression for the function $f(x)$;
(II) The number of years it takes for the tree to reach eight times its initial height.

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