
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 $f(x)=ax^{4}\ln x+bx^{4}-c$ $(x > 0)$, it attains an extremum of $-3-c$ at $x=1$, where $a,b,c$ are constants.

$(1)$ Determine the values of $a$ and $b$;

$(2)$ Discuss the monotonic intervals of the function $f(x)$;

$(3)$ If for any $x > 0$, the inequality $f(x)\geqslant -2c^{2}$ always holds, find the range of values for $c$.

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