
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 $f(x) = \ln(e^x + a)$ (where $a$ is a constant, $e=2.71828\ldots$) is an odd function over $\mathbb{R}$.

(Ⅰ) Find the value of $a$;  
(Ⅱ) Discuss the number of roots of the equation $\frac{\ln x}{f(x)} = x^2 - 2ex + m$ with respect to $x$.

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