
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 $f(x)$ satisfying the condition $f(x+y)=f(x)f(y)$ and $f(1)=1$, determine the value of $$ \frac {f^{2}(1)}{f(1)}+ \frac {f^{2}(2)}{f(3)}+ \frac {f^{2}(3)}{f(5)}+\ldots+ \frac {f^{2}(1009)}{f(2017)}. $$

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