
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 $f(x)= \begin{cases} \sqrt {x}+3,x\geqslant 0 \\ ax+b,x < 0 \end{cases}$ that satisfies the condition: for all $x_{1}∈R$ and $x_{1}≠ 0$, there exists a unique $x_{2}∈R$ and $x_{1}≠ x_{2}$ such that $f(x_{1})=f(x_{2})$, determine the value of the real number $a+b$ when $f(2a)=f(3b)$ holds true.

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