
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 $f(x)= \frac {\ln x}{x}+x-a$ ($a\in\mathbb{R}$) and the function $y= \frac {2e^{x+1}}{e^{2x}+1}$, determine the range of values for $a$ such that there exists a point $(x_{0},y_{0})$ on the curve where $f(f(y_{0}))=y_{0}$.

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