
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 a function $f(x)$ defined on the set of real numbers $\mathbb{R}$, which satisfies the following three conditions:
$(1) f(-1)=2$; $(2)$ When $x < 0$, $f(x) > 1$; $(3)$ For any real numbers $x$ and $y$, $f(x+y)=f(x)f(y)$;
$(1)$ Find the values of $f(0)$ and $f(-4)$;
$(2)$ Determine the monotonicity of the function $f(x)$, and find the solution set of the inequality $f(-4x^{2})f(10x)\geqslant \frac {1}{16}$.

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