
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 tetrahedron \( P-ABCD \), given vectors \(\overrightarrow{AB} = (4, -2, 3)\), \(\overrightarrow{AD} = (-4, 1, 0)\), and \(\overrightarrow{AP} = (-6, 2, -8)\), calculate the height \( h \).

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