
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 cube \(A B C D A_1 B_1 C_1 D_1\) with edge length \(a\), points \(M\) and \(K\) are the midpoints of edges \(A B\) and \(C D\) respectively. Find the radius of the sphere that passes through points \(M\), \(K\), \(A_1\), and \(C_1\).

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