
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 a triangular pyramid \( P-ABC \) with a base that is an equilateral triangle of side length \( 4\sqrt{3} \), and \( PA = 3 \), \( PB = 4 \), and \( PC = 5 \). If \( O \) is the centroid of \( \triangle ABC \), find the length of \( PO \).

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