
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 $f(x)=\begin{cases} & e^{x},x\geqslant 0 \\ & -x^{3},x < 0 \\ \end{cases}$, if $g(x)=f(f(x))-a(a > 0)$ has two distinct zeros $(x_{1})$, $(x_{2})$, calculate the maximum value of $(e^{x_{1}}\cdot e^{x_{2}})$.

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