
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 $f(x) = \frac{2x - m}{e^x}$, where $m$ is a constant,

(1) If the function $y = f(x)$ is monotonically decreasing on the interval $[1, e]$, find the range of values for the real number $m$.
(2) If $m > 0$ and the function $g(x) = \frac{|2x - m|}{e^x}$, find the minimum value $h(m)$ of the function $g(x)$ on the interval $[1, 2]$.

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