
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 $f(x) = e^x - ax$ (where $e$ is the base of the natural logarithm).  
(1) If $a=1$, find the minimum value of the function $f(x)$.  
(2) Given that $f(x) \geq 1$ for any real number $x$, find the value of the real number $a$.

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