
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
A smart ant, walking on the surface of the cube below, always travels the shortest possible path between two points. The cube has edges of length \(1 \, \text{cm}\).

![](https://cdn.mathpix.com/cropped/2024_05_01_d18780f0fd52e0502cf8g-03.jpg?height=571&width=662&top_left_y=1733&top_left_x=800)

What distance will the smart ant travel if it goes:

a) From vertex \(A\) to vertex \(B\) ?

b) From point \(M\) to point \(N\) ?

c) From vertex \(A\) to vertex \(D\) ?

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