
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 a cube $A C_{1}$, $M$ and $N$ are the midpoints of edges $C_{1} D_{1}$ and $A B$ respectively. The points $A_{1}, M, C,$ and $N$ lie in the same plane. Find the sine of the angle between $C D$ and the plane $A_{1} M C N$.

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