
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 point P is a point on the face BCD of a regular tetrahedron A-BCD, and the distances from P to the other three faces are $h_1$, $h_2$, and $h_3$ respectively, and the height of the regular tetrahedron A-BCD is $h$, determine the relationship between $h$ and the sum $h_1 + h_2 + h_3$.

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