
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
If there exists a real number $x_0$ in the domain of function $f(x)$ such that $f(x_0+1)=f(x_0)+f(1)$, then $x_0$ is called a "splittable point" of function $f(x)$. Find the range of values of $a$ for which the function $$f(x)=\log_{5} \frac {a}{2^{x}+1}$$ has a "splittable point".

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