
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 the triangular pyramid \( P-ABC \), \( PB \perp AC \) and \( PH \perp \) plane \( ABC \) at point \( H \) which lies inside \( \triangle ABC \). The angle between \( PB \) and the plane \( ABC \) is \( 30^{\circ} \). The area of \( \triangle PAC \) is 1. When the dihedral angle \( P - AC - B \) is \( \qquad \), the area \( S_{\triangle ABC} \) is maximized.

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