
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 $f(x)$ with domain $\mathbb{R}$ that satisfies $f(a+b) = f(a)f(b)$ for all $a,b \in \mathbb{R}$, and $f(x) > 0$. If $f(1) = \frac{1}{2}$, then find the value of $f(-2)$.
A) $\frac{1}{2}$
B) $\frac{1}{4}$
C) 2
D) 4

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