
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
The base of a right prism \(A B C A_1 B_1 C_1\) is a right triangle \(A B C\) \((\angle B=90^\circ, A B=B C=10)\), and \(A A_1=B B_1=C C_1=12\). Point \(M\) is the midpoint of the lateral edge \(A A_1\). Through points \(M\) and \(B_1\), a plane is drawn that forms a \(45^\circ\) angle with the plane of the base and intersects the edge \(C C_1\) at point \(E\). Find \(C E\).

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