
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 $f(x) = \frac{e^x}{e^x}$.
(I) Find the extreme values of the function $f(x)$;
(II) If the line $y = ax + b$ is the tangent to the graph of the function $f(x)$, determine whether $a - b$ has a maximum value. If it does, find the maximum value; if not, explain the reason.
(III) Find all solutions to the equation $f[f(x)] = x$.

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