
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
The base side length of the regular triangular prism \( ABC-A_1B_1C_1 \) is \( a \), and the side edge length is \( \sqrt{2}a \). Find the angle between \( AC_1 \) and the lateral face \( ABB_1A_1 \).

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