
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 $f(x)= \frac{16}{x} + x^2$ for $x \in (0, +\infty)$,
(1) Using the definition of function monotonicity, determine the intervals where $f(x)$ is monotonic;
(2) Let the function $g(x)=|\log_{10}x|$. If $0 < a < b$ and $g(a) = g(b)$, find the range of possible values for $a^2 + 16b$.

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