
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 A be any point on curve M, and B be any point on curve N. If the minimum value of |AB| exists and is d, then d is called the distance between curve M and curve N.
(1) If curve M is y = e^x (e is the base of the natural logarithm), and curve N is y = x, then the distance between curve M and N is ______;
(2) If curve M is y^2 + 1 = x, and curve N is x^2 + 1 + y = 0, then the distance between curve M and N is ______.

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