
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 triangular prism \( P-ABC \), \( PA \perp \) plane \( ABC \), and \( AC \perp BC \). Given \( AC = 2 \), the dihedral angle \( P-BC-A \) is \( 60^\circ \), and the volume of the triangular prism \( P-ABC \) is \( \frac{4\sqrt{6}}{3} \). Find the sine value of the angle between line \( PB \) and plane \( PAC \).

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