
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 $f(x)=\left\{{\begin{array}{l}{(a-3)x+2a, x<1}\\{a{x^2}+(a+1)x, x\geq 1}\end{array}}\right.$ is a monotonically increasing function on $R$, determine the range of real number $a$.

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