
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 $f(x)= 
\begin{cases} 
(5-a)x+1, & x < 1 \\
a^{x}, &x \geq 1
\end{cases}
(a > 0,a \neq 1)$ is an increasing function on $\mathbb{R}$, then the range of the real number $a$ is _______.

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