
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 right triangular prism $ABC-{A_1}{B_1}{C_1}$, $CA=CB=1$, $\angle BCA={90}^{\circ }$, $A{A_1}=2$, points $M$ and $N$ are the midpoints of ${{A_1}{B_1}}$ and ${{A_1}A}$ respectively. Find the cosine value of the angle formed by the skew lines ${{A_1}B}$ and ${{B_1}C}$.

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