
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 $\mathbb{R}$ that satisfies the following three conditions:
1. $f(-1) = 2$;
2. For $x < 0$, $f(x) > 1$;
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 solve the inequality $f(-4x^2)f(10x) \geq \frac{1}{16}$.

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