
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
(1) Find the derivative of the function $y=(2x^2-3)\sqrt{1+x^2}$.
(2) Let the function $f(x)=(x\ln x)^{-1}$ for $x>0$ and $x\neq 1$. Determine the intervals of monotonicity for the function $f(x)$.

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