
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 the function $f(x) = \frac{x-e}{e^x}$ (where $e$ is the base of the natural logarithm).

(Ⅰ) Find the intervals of monotonicity and the maximum value of $f(x)$;

(Ⅱ) If for any $x \in (0, +\infty)$, $2|\ln x - \ln 2| \geqslant f(x) + c - \frac{1}{e^2}$ always holds, find the range of the real number $c$.

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