
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
In the rectangular parallelepiped $ABCD A_1 B_1 C_1 D_1$, it is known that $AB=AA_1=12$ and $AD=30$. Point $M$ is located on the face $ABB_1A_1$ at a distance of 1 from the midpoint of $AB$ and at equal distances from the vertices $A$ and $B$. Point $N$ lies on the face $DCC_1D_1$ and is symmetrically located to point $M$ with respect to the center of the parallelepiped. Find the shortest path on the surface of the parallelepiped between points $M$ and $N$.

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