
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 triangular prism $ABC$($A\_1B\_1C\_1$), where the side edges and base edges are all equal, the projection of $A\_1$ on the base $ABC$ is the midpoint of $BC$. The cosine value of the angle formed by the skew lines $AB$ and $CC\_1$ is to be found.

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