
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
Let the function $f(x)= \begin{cases} 3^{x}+4a, & x > 3\\ 2x+a^{2}, & x\leqslant 3 \end{cases}$, where $a > 0$, if the range of $f(x)$ is $\mathbb{R}$, then the range of the real number $a$ is ______.

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