
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 $f(x) = |\ln|x-1||$, let $x\_1$, $x\_2$, $x\_3$, $x\_4$ be the four zero points of $f(x) - m$, and $k = \frac{1}{x\_1} + \frac{1}{x\_2} + \frac{1}{x\_3} + \frac{1}{x\_4}$. Find the value of $f(k) - e^k$.

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