
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 \( ABCD - A_1B_1C_1D_1 \) be a cube with edge length 1. The endpoint \( M \) of the line segment \( MN \) is on the ray \( AA_1 \), and the point \( N \) is on the ray \( BC \). Furthermore, \( MN \) intersects the edge \( C_1D_1 \) at point \( L \). Determine the minimum length of \( MN \).

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