
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
\( \triangle ABC \) is an equilateral triangle with side length 1, and \( PA \perp \) plane \( ABC \) with \( PA = \frac{\sqrt{6}}{4} \). Let \( A' \) be the reflection of point \( A \) across the plane \( PBC \). Find the angle between the line \( A'C \) and \( AB \).

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