
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 a function $f(x)$ whose derivative $f'(x) = e^x - 1$ (where $e$ is the base of the natural logarithm and $f(x)$ has no constant term),
(1) Find the minimum value of $f(x)$;
(2) If for any $x$ in $[0, 2]$, the inequality $f(x) \geq ax$ always holds, determine the range of the real number $a$.

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