
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 function $f(x)$ satisfies $f\left(1+ \frac {1}{x}\right) = \frac {1}{x^{2}} - 1$.  
(1) Find the explicit formula for $f(x)$.  
(2) If $g(x) = \frac {ax^{2} + x}{f(x)}$ is monotonically increasing in the interval $(2, +\infty)$, find the range of values for $a$.

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