
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 that the function $f(x)$ is an odd function defined on $[-e, 0) \cup (0, e]$, and when $x \in (0, e]$, $f(x) = ax + \ln x$.

(Ⅰ) Find the explicit formula for $f(x)$;  
(Ⅱ) Determine whether there exists a real number $a$ such that when $x \in [-e, 0)$, the minimum value of $f(x)$ is 3. If it exists, find the value of $a$; if not, explain why.

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