
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 $ABCD\_\\(A\_1\\)B\_\\(A\_1\\)C\_\\(A\_1\\)D\_\\(A\_1\\)$, where edges $AB$, $AD$, and $AA\_1$ lie on the axes of a three-dimensional Cartesian coordinate system, and the cube's edge length is one unit, find the coordinates of the midpoint of edge $CC\_1$.

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