
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 that the function $f(x)$ satisfies $f(a+b)=f(a) \cdot f(b)$ for all real numbers $a$ and $b$, $f(1)=2$, and $f(x)$ is always nonzero, the general term of the sequence ${a_n}$ is $a_n=\frac{f^2(n)+f(2n)}{f(2n-1)}$ ($n \in \mathbb{N}_+$). Find the sum of the first $n$ terms of the sequence ${a_n}$.

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