
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 that for any $x \in \mathbb{R}$, $e^{x} \geqslant ax+b$ always holds.  
(1) If $a=e$, then the maximum value of $b$ is \_\_\_\_\_\_;  
(2) Among all the values of $a$ and $b$ that satisfy the condition, the minimum value of $a-b$ is \_\_\_\_\_\_.

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