
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 $f(x)$ satisfies: $f(x+y)=f(x)f(y)$ and $f(1)=1$, calculate the value of $\dfrac {f^{2}(1)+f(2)}{f(1)}+ \dfrac {f^{2}(2)+f(4)}{f(3)}+ \dfrac {f^{2}(3)+f(6)}{f(5)}+\ldots+ \dfrac {f^{2}(1009)+f(2018)}{f(2017)}$.

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