
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 $a$ be a real number. If the function $f(x)$, defined by $f(x)=\left\{{\begin{array}{l}{x-{e^x}+2, x\leq 0}\\{\frac{1}{3}{x^3}-4x+a, x>0}\end{array}}\right.$, has exactly one zero, determine the range of values for $a$.

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