
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 $f(x) = \begin{cases} 2x^{3}+x^{2}+1,x\leqslant 0 \\ e^{ax},x > 0\\ \end{cases}$, find the range of the real number $a$ such that the maximum value of $f(x)$ on $[-2,3]$ is $2$.

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