
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 $f(x)=\ln x-ax^{2}+1$.
(1) Find the value of $a$ if the function takes an extreme value at $x=4$.
(2) Find the range of values of $a$ if the function $f(x)$ is monotonically decreasing in the interval $(3,+\infty)$.

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