
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 a unit cube $A B C D-A' B' C' D'$ with a point $M$ on the side $A A' B' B$ such that the distance from $M$ to the lines $A B$ and $B' C'$ are equal. Find the minimum distance from $M$ to the point $C'$.

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