
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) = $$\begin{cases} \overset{-x+10,x>a}{x^{2}+2x,x\leq a}\end{cases}$$, find the range of values for the real number $a$ such that for any $b$, there exists a real number $x_0$ that makes f($x_0$) = $b$ hold true.

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