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

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