
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 that \( A B C-A_{1} B_{1} C_{1} \) is a regular triangular prism with \( A B = B C = C A = 2 \) and \( A A_{1} = \sqrt{2} \), and \( D \) and \( E \) are the midpoints of \( A C \) and \( B C \), respectively, find the angle in degrees between \( A_{1} D \) and \( C_{1} E \).

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