
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 $f(x)=\left\{\begin{array}{l}-ax+3, x<a,\\(x-3){e}^{x}+{e}^{2}, x\geq a.\end{array}\right.$, if $f(x)$ has a minimum value, write down one value of $a$ that satisfies the condition as ______; the maximum value of $a$ is ______.

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